SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

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                                    FORM 6-K
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                        REPORT OF FOREIGN PRIVATE ISSUER
                      PURSUANT TO RULE 13a-16 OR 15d-16 OF
                       THE SECURITIES EXCHANGE ACT OF 1934


                                For June 3, 2004



                                  CNOOC Limited

                 (Translation of registrant's name into English)
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                                   65th Floor
                               Bank of China Tower
                                 One Garden Road
                               Central, Hong Kong
                    (Address of principal executive offices)

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(Indicate by check mark whether the registrant files or will file annual
reports under cover Form 20-F or Form 40-F)



                Form 20-F     X                Form 40-F
                              ---------                     ----------


(Indicate by check mark whether the registrant by furnishing the information
contained in this Form is also thereby furnishing the information to the
Commission pursuant to Rule 12g3-2(b) under the Securities Exchange Act of
1934.)


                Yes                            No             X
                              ---------                     ----------


(If "Yes" is marked, indicate below the file number assigned to the
registrant in connection with Rule 12g3-2(b): N/A.)







Company Press Release
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                 CNOOC Made New Oil Findings in South China Sea

(Hong Kong, June 2, 2004) - CNOOC Limited (together with its subsidiaries, the
"Company", NYSE: CEO, SEHK: 883) announced today that a wildcat well drilled on
HZ ("Huizhou") 26-3 in the Pearl River Mouth Basin of South China Sea was
successful.

HZ 26-3-1 is located in the Huizhou trough in the eastern South China Sea, about
170 kilometers southeast of Hong Kong. It was drilled to a total depth of 3,780
meters in 110 meters water depth. During the drill stem tests on a 7.94 mm
choke, it flowed over 1,400 barrels of 41-43 degree light gravity crude and
nearly 2 million cubic feet gas per day.

Mr. Zhang Guohua, Senior Vice President of Exploration of the Company,
commented, "Positive exploration results through independent activities in the
area will help maintain the Eastern South China Sea as a core production basin
for CNOOC Limited. Successes of this nature will generate further exploration
interests in the area."

The Company owns a 100% interest in the discovery.


Ends

Notes to Editor

CNOOC LIMITED - BACKGROUND
Incorporated in Hong Kong in August 1999, CNOOC Limited (SEHK: 883; NYSE: CEO)
is the dominant producer of crude oil and natural gas offshore China. CNOOC
Limited is also one of the largest independent crude oil and gas exploration and
production companies in the world.

As of December 31, 2003, its net proved reserves were 2.1 billion barrels-of-oil
equivalents. Daily production for the quarter ended March 31, 2004 was 362,672
BOE (unaudited).

CNOOC Limited is currently engaged in exploration, development and production in
four major areas offshore China, which cover Bohai Bay, Western South China Sea,
Eastern South China Sea and East China Sea. The Company is also one of the
largest offshore crude producers in Indonesia.

The Company has about 2,447 employees.


CNOOC LIMITED -RELATIONSHIP WITH ITS PARENT COMPANY
CNOOC Limited, incorporated in Hong Kong, is a 70.6% held subsidiary of China
National Offshore Oil Corporation ("CNOOC"). CNOOC Limited is the sole vehicle
through which CNOOC carries out oil and gas exploration, development, production
and selling activities offshore China and internationally.







CNOOC, the parent company, is involved in the administrative, research, and
services functions for the China offshore petroleum industry as well as other
mid- or downstream petroleum projects.

*** *** ***


This press release contains statements that are not historical facts, including
statements about beliefs and expectations of the directors of CNOOC Limited (the
Company). These forward-looking statements are based on current plans, estimates
and projections, and therefore you should not place undue reliance on them.
Forward-looking statements speak only as of the date they are made, and the
directors of the Company undertake no obligation to update publicly any of them
in light of new information or future events. Forward-looking statements involve
inherent risks and uncertainties. You are cautioned that a number of important
factors could cause actual results to differ materially from those contained in
any forward-looking statement. Such factors include, but are not limited to,
changes in PRC economic, political and social conditions as well as government
policies.

*** *** ***

For further enquiries, please contact:

Mr. Xiao Zongwei
CNOOC Limited
Tel : +86 10 8452 1646
Fax:  +86 10 8452 1441
E-mail:  xiaozw@cnooc.com.cn
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Ms Anne Lui/Ms. Charlotte Kong/Ms. Joe Lee
Ketchum Newscan Public Relations
Tel: 852-3141-8016/852-3141-8063/852-3141-8028
Fax: 852-2510-8199
E-mail:  anne.lui@knprhk.com
         -------------------
         Charlotte.kong@knprhk.com
         -------------------------
         joy.lee@knprhk.com
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                                   SIGNATURES

         Pursuant to the requirements of the Securities Exchange Act of 1934, as
amended, the registrant has duly caused this report on Form 6-K to be signed on
its behalf by the undersigned, thereunto duly authorized.

                                  CNOOC Limited


                                  By:  /s/ Cao Yunshi
                                       -----------------------------
                                       Name:   Cao Yunshi
                                       Title:  Company Secretary

Dated: June 3, 2004