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                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549


                                   FORM N-CSR


   CERTIFIED SHAREHOLDER REPORT OF REGISTERED MANAGEMENT INVESTMENT COMPANIES


                  Investment Company Act file number: 811-05617


                            TAIWAN GREATER CHINA FUND
               (Exact name of registrant as specified in charter)

                             Bank Tower, 10th Floor
                             205 Tun Hwa North Road
                               Taipei, Taiwan 105
                                Republic of China
                    (Address of principal executive offices)      (Zip code)

                         Citigate Financial Intelligence
                          111 River Street, Suite 1001
                            Hoboken, New Jersey 07030
                     (Name and address of agent for service)

       Registrant's telephone number, including area code: 1-800-343-9567


                   Date of fiscal year end: DECEMBER 31, 2004

                   Date of reporting period: JUNE 30, 2004






ITEM 1.  REPORTS TO STOCKHOLDERS.

TAIWAN GREATER CHINA FUND
www.taiwangreaterchinafund.com

TAIWAN OFFICE:
Room 1001, 205 DunHua North
Road Taipei, Taiwan, Republic of
China Tel: 886-2-2715-2988 Fax: 886-
2-2715-3166

OFFICERS AND TRUSTEES:
David N. Laux, Chairman and Trustee
    Steven R. Champion, President and Chief
Executive Officer Edward B. Collins,  Trustee
and  Audit  Committee   Member  Frederick  C.
Copeland,  Jr.,  Trustee and Audit  Committee
Member  Robert P.  Parker,  Trustee and Audit
Committee Member  Cheng-Cheng  Tung,  Trustee
Cheryl  Chang,   Chief   Financial   Officer,
Treasurer and Secretary

CUSTODIAN:
Central Trust of China
49 Wuchang Street, Sec.
1 Taipei, Taiwan
Republic of China

TRANSFER AGENT, PAYING
AND PLAN AGENT:
EquiServe Trust Company,
N.A. P.O. Box 43011
Providence, RI 02940-3011
U.S.A.
Telephone: 1-800-426-5523

TAIWAN ADMINISTRATOR:
International Investment Trust Company
Limited 17th Floor 167 FuXing North Road
Taipei, Taiwan, Republic of China Telephone:
886-2-2713-7702

U.S. ADMINISTRATOR:
Citigate Financial
Intelligence 111 River Street,
Suite 1001 Hoboken, NJ
07030 U.S.A.
Telephone: (201) 499-3500

U.S. LEGAL COUNSEL:
Paul, Weiss, Rifkind, Wharton & Garrison
LLP 1285 Avenue of the Americas New
York, NY 10019-6064
Telephone: (212) 373-3000

For information on the Fund, including
the NAV, please call toll free
1-800-343-9567.

[LOGO: TAIWAN GREATER CHINA FUND]

SEMI-ANNUAL REPORT
  June 30, 2004




DEAR STOCKHOLDERS

During the second quarter of 2004, the Taiwan
Stock Exchange (TSE) index declined 12.4% in
U.S. dollar terms, closing at 5839. This
compares to a 10.5% decline in the Fund's
share price on the New York Stock Exchange
and a 12.5% decline in its net asset value on
the same basis for this period.

The Fund's discount to net asset value based
on daily closing prices averaged 11.7% during
the quarter and reached a high of 14.9% on
June 9th. The discount reached its minimum
for the quarter on June 28th, closing at 5.9%
after the shares traded intraday at 5.2%. In
line with its goal of enhancing shareholder
value, the Fund announced on June 23rd that
it would conduct a self-tender for up to
one-third of its shares at 99% of net asset
value.

The second quarter represents the Fund's
first full reporting period under its new
management structure and investment strategy
of investing primarily in Taiwan-listed
companies operating in or exporting to China.
We will soon be tracking the Fund against the
Taiwan China Strategy index, which we have
developed with Morgan Stanley Capital
International. The principal differences
between this new custom index and the TSE
index are the heavier weighting of technology
stocks and the absence of shares of financial
institutions in the Taiwan China Strategy
index.

Despite continuing improvement in the economy
and positive results for many major listed
companies, Taiwan's market weakened for most
of the period as the TSE index declined each
month and all sectors dropped. The fall-off
in trading was pronounced: average daily
turnover value on a monthly basis dropped
more than 50% from March to June. The second
quarter also saw consecutive monthly net
sales by foreign institutional investors in
April and May; over the whole period net
sales totaled about US$2.5 billion compared
to approximately US$3.3 billion in net
purchases by such investors in the first
quarter.

Nevertheless, the market made a strong start
and climbed in the first half of April to a
quarterly peak of 6916 on April 15th on
positive U.S. economic news. American job
growth reached a four-year high in March, and
one measure showed services industry growth
advanced to a new record. Additionally,
several major TSE-listed companies such as
China Steel and Taiwan Semiconductor Mfg. Co.
(TSMC), a technology bellwether, reported
sound first-quarter results.

The Taiwan market reversed course in
mid-April following a sharp drop in spot
prices of the most widely used computer
memory chips. Investors grew increasingly
concerned about several developments that
contributed to market weakness for the rest
of the quarter. Most important were measures
taken in China to cool the economy of that
country, which is Taiwan's biggest export
market and the destination of most of its
external investment. These measures included
raising bank reserve requirements and curbs
on lending to various industries such as
steel, cement and property development.

Investor nervousness also focused on
record-high oil prices and the growing
likelihood that U.S. interest rates would
rise since both these developments could
result in increased costs and a slowdown in
aggregate demand. Several international
investment banks, citing possible inventory
increases, warned of slowing growth as they
downgraded various technology stocks.

Many major listed companies, however,
continued to report solid performance.
Several of Taiwan's semiconductor producers
achieved record-high revenue in April. AU
Optronics, one of the world's biggest
flat-panel display makers, saw sales more
than double in May




compared to the year earlier. That same
month, revenues of Formosa Chemicals & Fiber
and Nan Ya Plastics increased 49% and 38%,
respectively, from May 2003. And TSMC's
plants operated at more than full capacity
during the second quarter.

Taiwan's economy continued to steam ahead.
The official forecast estimates second
quarter growth of 6.8% from the year earlier
period after a 6.3% advance in the first
quarter. Foreign demand remained strong and
helped spur private investment. Merchandise
exports, equivalent to about half of gross
national product, surged 29% from the
corresponding quarter in 2003 and surpassed
the 23% increase in the previous quarter.
Continuing a trend over the last few years,
this performance was primarily due to a 43%
rise in shipments to China (including Hong
Kong), whose share of Taiwan's total exports
reached 37%. Private consumption growth
improved from 3.1% in the first quarter to an
estimated 4.3%, and private investment most
likely exceeded the officially projected 29%
rise, as indicated by the 54% increase in
second quarter imports of capital goods.

The Fund's returns remain highly correlated
with the TSE index with an R2 of 0.96. The
Fund's volatility remains very close to the
TSE index with a beta of 1.01.

Taiwan listed companies are now, in general,
excellent values, selling at a price-earnings
ratio of 16 compared to 20 for the Standard &
Poor's 500 and 47 for the Nasdaq Composite,
and yielding 3.1% compared to 1.7% for the
S&P and less than 0.5% for the Nasdaq.

As manager of the Fund, I will be working to
improve performance, reduce expenses and
reduce or eliminate the discount to net asset
value.

As David Laux, chairman of the Fund, recently
noted, "The growth in Taiwan's exports to
China over the past year has been more than
40%. The top three exporters from China are
Taiwan-invested firms. An astounding 70% of
China's computer and computer
hardware-related exports come from
Taiwan-invested firms in China. This trend is
not only continuing, it is accelerating. Our
Fund is focused on this phenomenon and
provides investors with an opportunity to
invest in the economies of both Taiwan and
China. We are excited about the prospects
ahead."

Respectfully submitted,

/s/ Steven R. Champion
Steven R. Champion
President and Chief
Executive Officer

July 30, 2004

p.s. We are enclosing with this report a
letter concerning your ability to participate
in the Fund's Dividend Reinvestment Plan.




Portfolio Highlights
Three Months Ended June 30, 2004


Key Statistics

Change in N.A.V. ($5.38 to $4.71)       -$0.67
Total Net Assets                        $154.2
                                        Million



Ten Largest Holdings
                                        Percent of
Company                                 Net Assets
Hon Hai Precision Industry Co., Ltd.    8.71%
China Steel Corp.                       8.48
Taiwan Semiconductor Manufacturing Co., 7.28
Ltd.
Formosa Chemicals & Fiber Corp.         4.79
AU Optronics Corp.                      4.66
Asustek Computer Inc.                   4.47
United Microelectronics Corp.           4.59
Nan Ya Plastics Corp.                   4.22
BenQ Corp.                              3.26
Formosa Plastics Corp.                  3.23
Security Classification
                                            Value
Percent of Net Assets                       (000)
Common Stocks                   98.70%      $152,153
Total Investments               98.70       152,153
Other Assets Less Liabilities   1.30        2,001
Net Assets                      100.00%     $154,154

Industry Diversification
                                            Percent of
                                            Net Assets
Computer Systems & Hardware                 17.87%
Semiconductors                              14.52
Plastics                                    13.05
ODM--Peripherals                             8.79
Steel & Other Metals                        8.48
Flat-Panel Displays                         7.76
Electronic Components                       4.11
Transportation                              3.90
Automobile                                  3.57
Food                                        2.62




TAIWAN   GREATER   CHINA  FUND
CONSOLIDATED SCHEDULE OF INVESTMENTS
(UNAUDITED) / JUNE 30, 2004

COMMON STOCKS-- 98.70%



                                                                                    % of          Market Value
                                                                                            
Automobile-- 3.57%                                                                  Net Assets    (U.S. Dollars)
219,000          shs.*  Tong Yang Industry Co., Ltd.                                0.23          $ 350,141
2,459,000        *      Yulon Motor Co., Ltd                                        1.76          2,708,358
1,791,000        *      China Motor Corp.                                           1.58          2,439,260
                                                                                                  5,497,759
Cement -- 2.03%
3,494,000        *      Taiwan Cement Corp.                                         1.02          1,572,429
2,786,000        *      Asia Cement Corporation                                     1.01          1,550,756
                                                                                                  3,123,185
Communications Equipment-- 2.13%
1,352,000        *      D-Link Corp.                                                1.02          1,573,164
392,000          *      Accton Technology Corp                                      0.14          218,197
743,000          *      Zyxel Communications Corp...                                0.97          1,495,899
                                                                                                  3,287,260
Computer Systems & Hardware-- 17.87%
3,625,584        *      Hon Hai Precision Industry Co., Ltd.                        8.71          13,418,150
1,596,000        *      Compal Electronics Inc.                                     1.12          1,724,767
832,000          *      Elitegroup Computer Systems Co., Ltd.                       0.26          396,600
1,075,000        *      Acer Sertek Inc.                                            0.98          1,505,477
1,091,000        *      Inventec Corp.                                              0.44          678,342
3,040,000        *      Asustek Computer Inc.                                       4.47          6,885,566
279,000          *      Giga-Byte Technology Co., Ltd.                              0.27          417,158
426,000          *      Arima Computer Corp.                                        0.09          131,174
1,033,000        *      Quanta Computer Inc.                                        1.42          2,186,810
84,000           *      Advantech Co., Ltd.                                         0.11          170,363
                                                                                                  27,514,407
Chemicals -- 0.43%
1,264,000               Eternal Chemical Co., Ltd.                                  0.43          669,892
Electrical & Machinery-- 2.51%
1,636,000        *      Teco Electric & Machinery Co., Ltd.                         0.34          527,976
7,782,000        *      Walsin Lihwa Corp.                                          2.17          3,340,903
                                                                                                  3,868,879
Electronic Components-- 4.11%
675,150                 Delta Electronics Inc.                                      0.55          843,563
1,022,000        *      Wus Printed Circuit Co., Ltd.                               0.35          529,534
4,850,000        *      Yageo Corp.                                                 1.61          2,484,234
151,000          *      Merry Electronics Co., Ltd.                                 0.22          344,249
124,000          *      Catcher Technology Co., Ltd.                                0.26          394,671
144,000          *      Largan Precision Co., Ltd.                                  0.89          1,377,113
271,000          *      Tripod Technology Corp.                                     0.23          352,240
                                                                                                  6,325,604


See accompanying notes to consolidated financial statements and accountants'
review report.




SCHEDULE OF INVESTMENTS (CONT'D.)


                                                                                            
Electronics -- 0.49%
470,000          shs.*  Synnex Technology International Corp.                     0.49            $ 758,401
Flat-Panel Displays-- 7.76%
506,000          *      Picvue Electronics Ltd.                                   0.09            140,077
4,753,000               AU Optronics Corp.                                        4.66            7,176,995
1,435,000        *      Chunghwa Picture Tubes, Ltd.                              0.48            743,523
1,971,000        *      Chi Mei Optoelectronics Corp.                             2.05            3,151,266
1,084,000        *      Quanta Display Inc.                                       0.48            744,598
                                                                                                  11,956,459
Food -- 2.62%
9,100,000        *      Uni-President Enterprise Corp.                            2.62            4,041,451
Glass-- 0.32%
623,160                 Taiwan Glass Ind. Corporation.                            0.32            496,314
ODM -- Peripherals -- 8.79%
4,583,000        *      Lite-on Technology Corp.                                  3.11            4,789,930
1,422,000        *      CMC Magnetics Corp.                                       0.48            736,788
4,971,000        *      Ritek Inc.                                                1.43            2,207,698
4,462,700               BenQ Corp.                                                3.26            5,020,950
644,000          *      Premier Image Technology Corp.                            0.51            781,762
                                                                                                  13,537,128
Plastics -- 13.05%
3,532,980               Formosa Plastics Corp.                                    3.23            4,968,662
4,962,920               Nan Ya Plastics Corp.                                     4.22            6,509,470
1,751,000        *      Taiwan Styrene Monomer Corp.                              0.81            1,254,603
4,754,000        *      Formosa Chemicals & Fiber Corp.                           4.79            7,389,637
                                                                                                  20,122,372
Retailing -- 0.53%
432,000          *      President Chain Store Corp.                               0.53            812,198
Rubber-- 1.23%
1,460,000        *      Cheng Shin Rubber Ind. Co., Ltd.                          1.23            1,901,999
Semiconductors -- 14.52%
9,558,000        *      United Microelectronics Corp.                             4.59            7,074,759
1,556,000        *      Advanced Semiconductor Engineering, Inc.                  0.79            1,225,451
781,000          *      Silconware Precision Industries Co., Ltd.                 0.40            610,463
7,836,614               Taiwan Semiconductor Manufacturing Co., Ltd.              7.28            11,229,966
1,865,000        *      Via Technologies Inc.                                     1.00            1,546,114
206,000          *      Sunplus Technology Co., Ltd.                              0.23            356,802
110,000          *      Novatek Microelectronics Corp.                            0.23            361,510
                                                                                                  22,405,065
Steel & Other Metals -- 8.48%
13,883,000       *      China Steel Corp.                                         8.48            13,071,189


See accompanying notes to consolidated financial statements and accountants'
review report.




TAIWAN GREATER CHINA FUND CONSOLIDATED SCHEDULE OF INVESTMENTS (UNAUDITED)
(CONTINUED) / JUNE 30, 2004


                                                                                             
Textiles -- 0.47%
1,237,000 shs.*         Far Eastern Textile Ltd.                                       0.47        $   728,832
Transportation-- 3.90%
1,948,000            *  Evergreen Marine Corp. (Taiwan) Ltd.                           1.06            1,637,993
2,720,000            *  Yang Ming Marine Transport Corp.                               1.62            2,496,521
1,192,000            *  China Airlines Ltd.                                            0.40            617,617
683,000              *  Wan Hai Lines Ltd.                                             0.39            602,617
1,595,000            *  Eva Airways Corp.                                              0.43            663,501
                                                                                                       6,018,249
Other -- 3.89%
3,485,000            *  Pou Chen Corp.                                                 2.10            3,239,941
879,000              *  Great China Metal Industry Co., Ltd.                           0.34            525,708
244,480                 Nien Made Enterprise Co., Ltd.                                 0.23            358,305
917,000              *  Giant Manufacturing Co., Ltd.                                  0.72            1,113,161



                                                                                                 
442,000              *  Taiwan Fu Hsing Industry Co., Ltd.                             0.26            405,685
341,000              *  Taiwan Hon Chuan Enterprise Co., Ltd.                          0.24            373,560
                                                                                                       6,016,360

TOTAL INVESTMENTS IN SECURITIES AT MARKET VALUE (COST                                  98.70        152,153,003
$173,964,073)
OTHER ASSETS (LESS LIABILITIES)                                                        1.30            2,001,445
NET ASSETS                                                                             100.00      $154,154,448


* Non-income producing: these stocks did not pay a cash dividend during the
six-month period.

See accompanying notes to consolidated financial statements and accountants'
review report.




TAIWAN GREATER CHINA FUND
CONSOLIDATED STATEMENT OF ASSETS AND LIABILITIES
JUNE 30, 2004 (UNAUDITED) (EXPRESSED IN U.S. DOLLARS)



                                                                                               
ASSETS
Investments in securities at market value (Notes 2B, 2C, 3 and 6):
Common stocks (cost-- $173,964,073)                                                               $152,153,003
Cash                                                                                              5,704,804
Dividends receivable                                                                              608,392
Office equipment (Note 2D)                                                                        31,690
Prepaid expense and other assets                                                                  34,241
Total assets                                                                                      158,532,130
LIABILITIES
Payable for investment securities purchased                                                       3,989,607
Administration fee payable (Note 4)                                                               25,454
Custodian fee payable (Note 5)                                                                    15,993
Professional fees payable                                                                         224,089
Accrued Republic of China taxes (Note 2H)                                                         106,001
Other accrued expense                                                                             16,538
Total liabilities                                                                                 4,377,682
Net assets                                                                                        $154,154,448


COMPONENTS OF NET ASSETS
Par value of shares of beneficial interest (Note 7)                                               326,990
Additional paid-in capital                                                                        306,652,438
Accumulated net investment income                                                                 1,368,792
Accumulated realized loss on investments                                                          (92,177,601)
Unrealized depreciation on investments (Note 6)                                                   (21,811,070)
Cumulative translation adjustment (Note 2F)                                                       (40,205,101)
Net assets                                                                                        $154,154,448

Net asset value per share (32,698,976 shares issued and outstanding, par value $0.01)             $4.71


See accompanying notes to consolidated financial statements and accountants'
review report.




TAIWAN GREATER CHINA FUND
CONSOLIDATED STATEMENT OF OPERATIONS
FOR THE SIX MONTHS ENDED JUNE 30, 2004 (UNAUDITED) (EXPRESSED IN U.S. DOLLARS)


                                                                                               
INVESTMENT INCOME (NOTE 2C)
Dividends                                                                                         $1,050,342
Interest                                                                                          22,940
Other                                                                                             54,448
                                                                                                  1,127,730

REPUBLIC OF CHINA TAXES (NOTE 2H)                                                                 319,685
                                                                                                  808,045
EXPENSES
Management fee (Note 4)                                                                           346,909

Self-management expenses (Note 1)
Personnel expenses                                                                                232,299
Rental expenses                                                                                   2,471
Research expenses                                                                                 14,514
Travel expenses                                                                                   61,605
Other expenses                                                                                    58,485

Custodian fee (Note 5)                                                                            114,830
Administrative fee (Note 4)                                                                       140,042
Audit fee                                                                                         71,128
Legal fees and expenses                                                                           423,896

Insurance expenses                                                                                42,484
Trustee fees and expenses (Note 8)                                                                103,630
Shareholder communication expenses                                                                35,809
Other expenses                                                                                    102,319
                                                                                                  1,750,421
Net investment loss                                                                               (942,376)
NET REALIZED AND UNREALIZED GAIN/LOSS ON INVESTMENTS AND FOREIGN CURRENCIES (NOTES 2E AND 6)
Net realized gain on:
investments                                                                                       23,835,262
foreign currency transactions                                                                     137,744
net realized gain on investments and foreign currency transactions                                23,973,006
Net changes in unrealized appreciation/depreciation on:
investments                                                                                       (37,191,220)
translation of assets and liabilities in foreign currencies                                       514,412
Net realized and unrealized loss from investments and foreign currencies                          (12,703,802)
Net decrease in net assets resulting from operations                                              $(13,646,178)



See accompanying notes to consolidated financial statements and accountants'
review report.




TAIWAN GREATER CHINA FUND

CONSOLIDATED STATEMENT OF CHANGES IN NET ASSETS
FOR THE SIX MONTHS ENDED JUNE 30, 2004, AND THE YEAR ENDED DECEMBER 31, 2003
(EXPRESSED IN U.S. DOLLARS)




                                                                         Six Months               Year Ended
                                                                         Ended June 30,           December 31,
                                                                                 2004             2003
                                                                         (Unaudited)
                                                                                            
NET INCREASE/DECREASE IN NET ASSETS RESULTING FROM OPERATIONS
Net investment loss                                                      $       (942,376)        $ (673,737)
Net realized gain/loss on investments and foreign currency
transactions                                                                     23,973,006       (11,991,683)
Unrealized appreciation/depreciation on investments.                             (37,191,220)     35,930,915
Unrealized appreciation on translation of
assets and liabilities in foreign currencies                                     514,412          3,561,353
Net increase/decrease in net assets resulting from operations                    (13,646,178)     26,826,848

Distribution to shareholders                                                    --                (1,961,939)

Net assets, beginning of period                                          167,800,626              142,935,717

Net assets, end of period                                                $154,154,448             $167,800,626



See accompanying notes to consolidated financial statements and accountants'
review report.




TAIWAN GREATER CHINA FUND
CONSOLIDATED FINANCIAL HIGHLIGHTS
(EXPRESSED IN U.S. DOLLARS)




                                                 Six Months Ended
                                                     June 30, 2004           Years Ended December 31,
                                                     (Unaudited)   2003      2002     2001      2000     1999

                                                                                       
PER SHARE OPERATING PERFORMANCE:
       Net asset value, beginning of period          5.13          4.37      5.40     5.78      10.23    7.53
       Net investment loss                           (0.03)        (0.02)    (0.06)   (0.05)    (0.11)   (0.11)
       Net realized and unrealized gain/loss
       on investments                                (0.41)        0.73      (1.02)   0.06      (3.56)   2.58
       Net realized and unrealized
       appreciation/depreciation on
       translation of foreign currencies             0.02          0.11      0.05     (0.39)    (0.41)   0.23
       Total from investment operations              (0.42)        0.82      (1.03)   (0.38)    (4.08)   2.70

DISTRIBUTIONS TO SHAREHOLDERS FROM:
       Net investment income                         --            (0.06)    --       --        --       --
       Net realized gain on investments              --            --        --       --        (0.37)   --
       Total distributions*                          --            (0.06)    --       --        (0.37)   --
NET ASSET VALUE, END OF PERIOD                       4.71          5.13      4.37     5.40      5.78     10.23
PER SHARE MARKET PRICE, END OF PERIOD                4.26          4.75      4.05     4.75      4.56     8.44

TOTAL INVESTMENT RETURN (%)**:
       Based on the Trust's market price             (10.32)       18.79     (14.74)  4.17      (41.71)  36.35
       Based on the Trust's net asset value          (8.19)        18.75     (19.07)  (6.57)    (39.94)  35.86
       U.S. $ return of Taiwan stock exchange
       index                                         (0.28)        35.32     (19.03)  10.16     (46.62)  35.15
RATIOS AND SUPPLEMENTAL DATA:
       Net assets, end of period (in thousands)   .. 154,154       167,801   142,936  176,526   188,939  334,521
       Ratio of expenses to average net assets (%)   2.06)+        2.57      2.19     2.01      1.67     1.81
       Ratio of net investment loss to
       average net assets (%)                        (1.10) +      (0.44)    (1.23)   (1.01)    (1.09)   (1.35)
       Portfolio turnover ratio (%)**                108           78        107      173       165      191




* See Note 2G for information concerning the Trust's distribution policy.

** Investment return and portfolio turnover ratio are calculated for the six
months ended June 30, 2004 (not annualized) and for each of the five years ended
December 31, 2003.

+      Annualized

See accompanying notes to consolidated financial statements and accountants'
review report.




TAIWAN GREATER CHINA FUND

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS / JUNE 30, 2004 (EXPRESSED IN U.S.
DOLLARS)

NOTE 1 -- ORGANIZATION AND ACQUISITION OF
THE TAIWAN (R.O.C.) FUND

The Taiwan Greater China Fund (the "Trust",
formerly known as The R.O.C. Taiwan Fund) is
a Massachusetts business trust formed in July
1988 and registered with the U.S. Securities
and Exchange Commission as a diversified,
closed-end management investment company
under the Investment Company Act of 1940. The
Trust changed its name from The R.O.C. Taiwan
Fund to the Taiwan Greater China Fund on
December 29, 2003. The change took effect on
the New York Stock Exchange on January 2,
2004. The Trust was formed in connection with
the reorganization (the "Reorganization") of
The Taiwan (R.O.C.) Fund (the "Fund"). The
Fund, which commenced operations in October
1983, was established under the laws of the
Republic of China as an open-end contractual
investment fund pursuant to an investment
contract between International Investment
Trust Company Limited ("IIT") and the Central
Trust of China, as custodian. Pursuant to the
Reorganization, which was completed in May
1989, the Trust acquired the entire
beneficial interest in the assets
constituting the Fund. On February 23, 2004,
the investment contract was terminated and
substantially all of the assets held in the
Fund were transferred to the direct account
of the Trust. The Trust thereupon converted
to internal management and now directly
invests in Taiwan as a Foreign Institutional
Investor ("FINI"). The Fund was subsequently
liquidated.

As required by the Trust's "Declaration of
Trust," if the Trust's shares trade on the
market at an average discount to NAV of more
than 10% in any consecutive 12-week period
after the most recent such vote, the Trust
must submit to the shareholders for a vote at
its next annual meeting a binding resolution
that the Trust be converted from a closed-end
to an open-end investment company. The
affirmative vote of a majority of the Trust's
outstanding shares is required to approve
such a conversion.

NOTE 2 -- SUMMARY OF SIGNIFICANT ACCOUNTING
POLICIES A -- Basis of presentation and
principles of consolidation -- The
accompanying consolidated financial
statements of the Trust have been prepared in
accordance with accounting principles
generally accepted in the United States of
America. The consolidated financial
statements include the accounts of the Fund
(operation ended February 22, 2004). All
significant inter-company transactions and
balances have been eliminated in consolidation.

B -- Valuation of investments -- Common
stocks represent securities that are traded
on the Taiwan Stock Exchange or the Taiwan
over-the-counter market. Except when price
movements are constrained by collars imposed
by Republic of China regulations, in which
case the Trust's Board of Trustees has
provided for the use of fair valuation
procedures, such securities are valued at the
closing market price, or, if not quoted at
the end of the period, generally at the last
quoted closing market price. Short-term
investments are valued at amortized cost,
which approximates market value. Under this
method, the difference between the cost of
each security and its value at maturity is
accrued into income on a straight-line basis
over the days to maturity.

C -- Security transactions and investment
income --Security transactions are recorded
on the date the transactions are entered into
(the trade date). Dividend income is recorded
on the ex-dividend date, and interest income
is recorded on an accrual basis as it is
earned.

D -- Office equipment -- Office equipment is
stated at cost less accumulated depreciation.
Depreciation is applied from the month such
assets were placed into service, using the
straight-line method over the respective
useful lives of such assets.

E -- Realized gains and losses -- Realized
gains and losses on securities transactions
are determined for financial reporting
purposes using the average-cost method for
the cost of investments. For federal income
tax purposes, realized gains and losses on
securities transactions are determined using
the first-in, first-out method. For the
fiscal year ended December 31, 2003, the
Trust generated a net capital loss of
$11,721,463, and maintained a cumulative
prior year capital loss carryover of
$105,731,250, resulting in a total capital
loss carryover of $117,452,713. This capital
loss carryover may be used to offset any
future capital gains generated by the Trust,
and, if unused, $89,141,756 of such loss will
expire on December 31, 2009, $16,589,494 of
such loss will expire on December 31, 2010,
and $11,721,463 of such loss will expire on
December 31, 2011.

F -- Foreign currency translation --
Substantially all of the Trust's income is
earned, and its expenses are partially paid,
in New Taiwan Dollars ("NT$"). The cost and
market value of securities, currency
holdings, and other assets and liabilities
which are denomi-




TAIWAN GREATER CHINA FUND

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS /
JUNE 30, 2004 (EXPRESSED IN U.S. DOLLARS)

nated in NT$ are reported in the accompanying
consolidated financial statements after
translation into United States Dollars based
on the closing market rate for United States
Dollars in Taiwan at the end of the period.
At June 30, 2004, this rate was approximately
NT$33.775 to $1.00. Investment income and
expenses are translated at the average
exchange rate for the period. Currency
translation gains or losses are reported as a
separate component of changes in net assets
resulting from operations. The Trust does not
separately record that portion of the results
of operations resulting from changes in
foreign exchange rates on investments from
the fluctuations arising from changes in
market prices of securities held. Such
fluctuations are included with the net
realized and unrealized gain or loss from
investments.

G -- Distributions to shareholders -- It is
the Trust's policy to distribute all ordinary
income and net capital gains calculated in
accordance with U.S. federal income tax
regulations. Such calculations may differ
from those based on U.S. generally accepted
accounting principles. Permanent book and tax
differences primarily relate to the treatment
of the Trust's gains from the disposition of
passive foreign investment company shares as
well as the nondeductibility of net operating
losses for U.S. federal income tax purposes.
Temporary book and tax differences are
primarily due to differing treatments for
certain foreign currency losses. The Trust
declared a dividend of $0.01 a share, payable
on July 30, 2004, to shareholders of record
on July 12, 2004 (ex-date July 8, 2004). The
dividend, in total amount of $326,990,
represents undistributed net investment
income totaling $299,668 as of December 31,
2003.

H -- Taxes -- The Trust intends to continue
to elect and to continue to qualify as a
regulated investment company under the
Internal Revenue Code of 1986, as amended
(the "Code"). If the Trust complies with all
of the applicable requirements of the Code,
it will not be subject to U.S. federal income
and excise taxes provided that it distributes
all of its investment company taxable income
and net capital gains to its shareholders.
The Republic of China ("R.O.C.") levies a tax
at the rate of 20% on cash dividends and
interest received by the Trust on investments
in R.O.C. securities. In addition, a 20% tax
is levied based on the par value of stock
dividends (except those which have resulted
from capitalization of capital surplus)
received by the Trust. For the six-month
period ended June 30, 2004, total par value
of stock dividends received was $536,229.
Realized gains on securities transactions are
not subject to income tax in the R.O.C.;
instead, a securities transaction tax of 0.3%
of the market value of stocks sold or
transferred, and 0.1% of the market value of
bonds and beneficial certificates sold or
transferred, is levied. Proceeds from sales
of investments are net of securities
transaction tax paid of $556,980 for the six
months ended June 30, 2004.

I -- Use of estimates -- The preparation of
financial statements in conformity with U.S.
generally accepted accounting principles
requires management to make estimates and
assumptions that affect the amounts reported
in the consolidated financial statements,
consolidated financial highlights and
accompanying notes. Actual results could
differ from those estimates.

NOTE 3 -- INVESTMENT CONSIDERATIONS Because
the Trust concentrates its investments in
publicly traded equity and debt securities
issued by R.O.C. corporations, its portfolio
involves considerations not typically
associated with investing in U.S. securities.
In addition, the Trust is more susceptible to
factors adversely affecting the R.O.C.
economy than a fund not concentrated in these
issuers to the same extent. Since the Trust's
investment securities are primarily
denominated in New Taiwan Dollars, changes in
the relationship of the New Taiwan Dollar to
the U.S. Dollar may also significantly affect
the value of the investments and the earnings
of the Trust.

NOTE 4 -- INVESTMENT AND ADMINISTRATIVE
MANAGEMENT
A -- As described in Note 1, the Trust's
investment management agreement with IIT (the
"Investment Contract") was terminated on
February 23, 2004, and the Trust was
converted to internal management. Before the
termination of the Investment Contract, the
Trust paid IIT a fee in NT$, which was
accrued daily and paid monthly in arrears, at
the annual rate of 1.35% of the net asset
value ("NAV") with respect to Trust assets
held in Taiwan under the Investment Contract
up to NT$6 billion, 1.15% of such NAV in
excess of NT$6 billion up to NT$8 billion,
0.95% of such NAV in excess of NT$8 billion
up to NT$10 billion and 0.75% of such NAV in
excess of NT$10 billion. B -- Upon the
termination of the Investment Contract, the
Trust entered into an administrative services
agreement with IIT. Pursuant to this
agreement, IIT provides clerical, accounting,
tax, regulatory compliance




TAIWAN GREATER CHINA FUND

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS /
JUNE 30, 2004 (EXPRESSED IN U.S. DOLLARS)

and other administrative services to the
Trust. The Trust pays IIT a fee for these
services in NT$ at an annual rate of 0.15% of
the Trust's average daily NAV.

NOTE 5 -- CUSTODIAN
Pursuant to a custodian contract, the Central
Trust of China ("CTC") serves as custodian of
the assets of the Trust held in the R.O.C.
The Trust pays CTC a monthly fee in NT$ at
the annual rate of 0.13% of the NAV of the
Trust's assets up to NT$6 billion, 0.12% of
such NAV in excess of NT$6 billion up to NT$8
billion, 0.11% of such NAV in excess of NT$8
billion up to NT$10 billion and 0.10% of such
NAV in excess of NT$10 billion. Before
February 22, 2004, pursuant to the Investment
Contract, the Trust paid CTC a monthly fee at
the annual rate of 0.15% of the NAV with
respect to Trust assets held in Taiwan under
the Investment Contract up to NT$6 billion,
0.13% of such NAV in excess of NT$6 billion
up to NT$8 billion, 0.11% of such NAV in
excess of NT$8 billion up to NT$10 billion
and 0.09% of such NAV in excess of NT$10
billion, subject to a minimum annual fee of
NT$2.4 million.

NOTE 6 -- INVESTMENTS IN SECURITIES
Purchases and proceeds from sales of
securities, excluding short-term investments,
for the six months ended June 30, 2004,
included approximately $186,109,778 for stock
purchases and approximately $184,922,448 for
stock sales, respectively.

At June 30, 2004, the cost of investments for
U.S. federal income tax purposes was
approximately equal to the cost of such
investments for financial reporting purposes.
At June 30, 2004, the unrealized depreciation
of $21,811,070 for financial reporting
purposes consisted of $435,182 of gross
unrealized appreciation and $22,246,252 of
gross unrealized depreciation.

NOTE 7 -- SHARES OF BENEFICIAL INTEREST
A -- The Trust's "Declaration of Trust"
permits the trustees to issue an unlimited
number of shares of beneficial interest or
additional classes of other securities. The
shares have a par value of $0.01, and no
other classes of securities are outstanding
at present. At June 30, 2004, 32,698,976
shares were outstanding. B --The Trust plans
to conduct a tender offer to purchase up to
one-third of the Trust's outstanding shares
at a price equal to 99% of the Trust's net
asset value per share at the conclusion of
such offer. The tender offer is expected to
commence during the first week in August and
be completed by mid-September.

NOTE 8 -- TRUSTEE FEES AND EXPENSES
The amount shown is comprised of trustee fees
and expenses, which included spousal travel
expenses through the meeting of the Board of
Trustees held in February 2004 but not, by
decision of the Board of Trustees,
thereafter. Aggregate trustee remuneration
for the six months ended June 30, 2004 was
$61,444.

The Trust and its predecessors, The Taiwan
(R.O.C.) Fund and The R.O.C. Taiwan Fund,
have been certified as distributing funds by
the Board of Inland Revenue of the United
Kingdom for the period from their inception
to December 31, 2003. The Trust intends to
apply for such status for succeeding
accounting periods.

Steven R. Champion has been the President,
Chief Executive Officer and portfolio manager
of the Trust since February 2004. He was
Executive Vice President of Bank of Hawaii
from 2001-2003 and Chief Investment Officer
of Aetna International from 1997-2001. Mr.
Champion also previously served as the
portfolio manager of the Taiwan (R.O.C.)
Fund, predecessor to the Trust, from 1987 to
1989, and President and portfolio manager of
the Trust from 1989 to 1992. Other positions
he has held include Vice Chairman of the Bank
of San Francisco, Chief International
Investment Officer at the Bank of America,
and Vice President and Country Manager in
Taiwan for Continental Illinois National
Bank.

             PROXY VOTING POLICY

The Trust's policy with regard to voting
stocks held in its portfolio is to vote in
accordance with the recommendations of
Institutional Shareholder Services, Inc.
("ISS") unless the Trust's portfolio manager
recommends to the contrary, in which event
the decision as to how to vote will be made
by the Executive Committee of the Trust's
Board of Trustees. A summary of the voting
policies followed by ISS may be found on the
Trust's website,
http://www.taiwangreaterchinafund.com, and a
more detailed description of those policies
is available on the website of the Securities
and Exchange Commission (the "Commission"),
http://www.sec.gov. Information concerning
how the Trust voted proxies relating to its
portfolio securities during the period from
July 1, 2003 through June 30, 2004 will be
available on or through the Trust's website
and on the Commission's website no later than
August 31, 2004.




2004 ANNUAL MEETING OF SHAREHOLDERS

On July 21, 2004, the Trust held an annual meeting to:

1. Elect two trustees.

2. Consider whether to convert the Trust from a closed-end investment company
into an open-end investment company. The Trust's Declaration of Trust required a
shareholder vote on this question, because the Trust's shares had traded at an
average discount of more than 10% to its net asset value over a 12-week-period
beginning after the most recent such vote.

The results of the shareholder votes are shown below. Proxies representing
26,496,035, or 81.03%, of the 32,698,976 eligible shares outstanding were voted
in respect of the election of trustees. The trustees of the Trust recommended
that shareholders vote against the conversion proposal, which would have
required the affirmative vote of a majority of the outstanding shares to pass.
Proxies representing approximately 37.80% of the outstanding shares were voted
for conversion.
                                             FOR                    WITHHELD


NOMINEES TO THE BOARD OF TRUSTEES

Frederick C. Copeland, Jr.                   18,089,745             8,406,290

David N. Laux                                18,086,346             8,409,689


Messrs. Edward P. Collins, Robert P. Parker and Cheng-Cheng Tung, whose terms
did not expire in 2004, remained trustees.


                                             FOR           AGAINST       ABSTAIN


CONVERSION OF THE TRUST FROM A CLOSED-END    12,360,670    9,589,039     15,185
TO AN OPEN-END INVESTMENT COMPANY

Proxies covering 4,531,141 shares, or 17.10% of the shares represented at the
meeting, were not voted on this issue.



                                [KPMG LETTERHEAD]



         Review Report of Independent Registered Public Accounting Firm

Trustees and Shareholders of the Taiwan
Greater China Fund

We have reviewed the accompanying consolidated statement of assets and
liabilities of the Taiwan Greater China Fund, a Massachusetts business trust
(the "Trust"), including the consolidated schedule of investments, as of June
30, 2004, and the related consolidated statements of operations and of changes
in net assets and the consolidated financial highlights for the six-month period
ended June 30, 2004. These consolidated financial statements and financial
highlights are the responsibility of the Trust's management.

We conducted our review in accordance with standards of the Public Company
Accounting Oversight Board (United States). A review of interim financial
information consists principally of applying analytical procedures to financial
data and making inquiries of persons responsible for financial and accounting
matters. It is substantially less in scope than an audit conducted in accordance
with the standards of the Public Company Accounting Oversight Board (United
States), the objective of which is the expression of an opinion regarding the
financial statements taken as a whole. Accordingly, we do not express such an
opinion.

Based on our review, we are not aware of any material modifications that should
be made to the consolidated financial statements and financial highlights
referred to above in order for them to be in conformity with U.S. generally
accepted accounting principles.

We have previously audited, in accordance with standards of the Public Company
Accounting Oversight Board (United States), the consolidated statement of
changes in net assets for the year ended December 31, 2003, and the consolidated
financial highlights for each of the years in the five-year period ended
December 31, 2003, and in our report dated January 5, 2004, we expressed an
unqualified opinion on the consolidated statement of changes in net assets and
financial highlights.

/s/  KPMG Certified Public Accountants

Taipei,
Taiwan July
21, 2004




ITEM 2.  CODE OF ETHICS.

Not applicable to this filing on Form N-CSR of a semi-annual report.


ITEM 3.  AUDIT COMMITTEE FINANCIAL EXPERT.

Not applicable to this filing on Form N-CSR of a semi-annual report.


ITEM 4.  PRINCIPAL ACCOUNTANT FEES AND SERVICES.

Not applicable to this filing on Form N-CSR of a semi-annual report.


ITEM 5.  AUDIT COMMITTEE OF LISTED REGISTRANTS.

Not applicable to this filing on Form N-CSR of a semi-annual report.


ITEM 6.  SCHEDULE OF INVESTMENTS.

Not yet applicable to the registrant.


ITEM 7. DISCLOSURE OF PROXY VOTING POLICIES AND PROCEDURES FOR CLOSED-END
        MANAGEMENT INVESTMENT COMPANIES.

Not applicable to this filing on Form N-CSR of a semi-annual report.


ITEM 8. PURCHASES OF EQUITY SECURITIES BY CLOSED-END MANAGEMENT INVESTMENT
        COMPANIES AND AFFILIATED PURCHASERS.

Not yet applicable to the registrant.


ITEM 9.  SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS.

Since the registrant filed its Definitive Proxy Statement with the Securities
and Exchange Commission on June 29, 2004, there have been no material changes to
the procedures by which shareholders may recommend nominees to the registrant's
board of trustees.


ITEM 10.  CONTROLS AND PROCEDURES.

(a) The registrant's principal executive officer and principal financial officer
have concluded that the registrant's disclosure controls and procedures (as
defined in Rule 30a-3(c) under the Investment Company Act of 1940) are effective
as of a date within 90 days of the filing date of this report based on their
evaluation of such disclosure controls and procedures as required by Rule
30a-3(b) under the Investment Company Act of 1940 and Rule 13a-15(b) under the
Securities Exchange Act of 1934.

(b) There were no changes in the registrant's internal controls over financial
reporting (as defined in Rule 30a-3(d) under the Investment Company Act of 1940)
that occurred



during the registrant's most recent fiscal half-year that have materially
affected, or are reasonably likely to materially affect, such internal controls.


ITEM 11.  EXHIBITS.

(a)(1) CODE OF ETHICS REQUIRED BY ITEM 2 OF FORM N-CSR:

Not applicable to this filing on Form N-CSR of a semi-annual report.

(a)(2) CERTIFICATIONS REQUIRED BY RULE 30A-2(A) UNDER THE INVESTMENT COMPANY ACT
OF 1940:

See Exhibit 99.Cert attached hereto.

(b) CERTIFICATIONS REQUIRED BY RULE 30A-2(B) UNDER THE INVESTMENT COMPANY ACT OF
1940 AND RULE 13A-14(B) UNDER THE SECURITIES EXCHANGE ACT OF 1934:

See Exhibit 99.906Cert attached hereto.





                                   SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934 and the
Investment Company Act of 1940, the registrant has duly caused this report to be
signed on its behalf by the undersigned, thereunto duly authorized.

Taiwan Greater China Fund

By:  /s/ Steven R. Champion
     ------------------------------
     Name: Steven R. Champion
     Title: Chief Executive Officer and President

Date: August 13, 2004


Pursuant to the requirements of the Securities Exchange Act of 1934 and the
Investment Company Act of 1940, this report has been signed below by the
following persons on behalf of the registrant and in the capacities and on the
dates indicated.

By:  /s/ Steven R. Champion
     ------------------------------
     Name: Steven R. Champion
     Title: Chief Executive Officer and President


By:  /s/ Cheryl Chang
     -------------------------------
     Name: Cheryl Chang
     Title: Chief Financial Officer

Date: August 13, 2004