EXHIBIT 32.2 

CERTIFICATION BY CHIEF FINANCIAL OFFICER
PURSUANT TO 18 U.S.C. SECTION 1350,
AS ADOPTED PURSUANT TO
SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Annual Report of Frontier Oil Corporation (the “Company”) on Form 10-K for the period ending December 31, 2003 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Julie H. Edwards, Executive Vice President - Finance & Administration, Chief Financial Officer of the Company, certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, to my knowledge, 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.

/s/  Julie H. Edwards
Julie H. Edwards
Executive Vice President - Finance & Administration,
Chief Financial Officer

March 8, 2004