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 Quarterly Report of Frontier Oil Corporation (the “Company”) on Form 10-Q for the period ending March 31, 2005, 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 results of operations of the Company.

/s/ Julie H. Edwards

Julie H. Edwards

Executive Vice President - Finance & Administration,

Chief Financial Officer

May 6, 2005