General Maritime Subsidiary (GMR) 10-Q 2004 Q3 Quarterly report

Exhibit 32.1

CERTIFICATION OF THE PRINCIPAL EXECUTIVE OFFICER

CHIEF EXECUTIVE OFFICER CERTIFICATION

In connection with the quarterly report of General Maritime Corporation (the “Company”) on Form 10-Q for the three months ending September 30, 2004, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), the undersigned Chief Executive Officer of the Company, hereby certifies pursuant to 18 U.S.C. § 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

(1)The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2)The information contained in the Report fairly presents, in all material respects, the financial condition and result of operations of the Company.

This certification is made solely for purpose of 18 U.S.C. Section 1350, and not for any other purpose.

November 9, 2004

/s/ Peter C. Georgiopoulos

Peter C. Georgiopoulos

Chairman, Chief Executive

Officer, and President