EXHIBIT 32.2

Certification Of 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, 2004 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 2, 2005