**EXHIBIT
31.1**
 
 **Certification
By Chief Executive Officer**
 **Pursuant
To Rule 13a-14(a) and 15d-14(a) Under The Exchange Act**
 
 I, James
R. Gibbs, Chairman of the Board, President and Chief Executive Officer of
Frontier Oil Corporation, certify that:
 
 1.
    I
      have reviewed this annual report on Form 10-K of Frontier Oil
      Corporation;
 
 2.
    Based
      on my knowledge, this report does not contain any untrue statement of a
      material fact or omit to state a material fact necessary to make the
      statements made, in light of the circumstances under which such statements
      were made, not misleading with respect to the period covered by this
      report;
 
 3.
    Based
      on my knowledge, the financial statements, and other financial information
      included in this report, fairly present in all material respects the
      financial condition, results of operations and cash flows of the
      registrant as of, and for, the periods presented in this
      report;
 
 4.
    The
      registrant’s other certifying officers and I are responsible for
      establishing and maintaining disclosure controls and procedures (as
      defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) and internal
      control over financial reporting (as defined in Exchange Act Rules
      13a-15(f) and 15d-15(f)) for the registrant and
have:
  a) Designed
such disclosure controls and procedures, or caused such disclosure controls and
procedures to be designed under our supervision, to ensure that material
information relating to the registrant, including its consolidated subsidiaries,
is made known to us by others within those entities, particularly during the
period in which this report is being prepared;
  b)  Designed
such internal control over financial reporting, or caused such internal control
over financial reporting to be designed under our supervision, to provide
reasonable assurance regarding the reliability of financial reporting and the
preparation of financial statements for external purposes in accordance with
generally accepted accounting principles;
 
 c)  Evaluated
the effectiveness of the registrant’s disclosure controls and procedures and
presented in this report our conclusions about the effectiveness of the
disclosure controls and procedures, as of the end of the period covered by this
report based on such evaluation; and
 
 d)  Disclosed
in this report any change in the registrant’s internal control over financial
reporting that occurred during the registrant’s most recent fiscal quarter (the
registrant’s fourth fiscal quarter in the case of an annual report) that has
materially affected, or is reasonably likely to materially affect, the
registrant’s internal control over financial reporting; and
 
 5.
    The
      registrant’s other certifying officers and I have disclosed, based on our
      most recent evaluation of internal control over financial reporting, to
      the registrant’s auditors and the audit committee of the registrant’s
      board of directors (or persons performing the equivalent
      functions):
 
 a) All
significant deficiencies and material weaknesses in the design or operation of
internal control over financial reporting which are reasonably likely to
adversely affect the registrant’s ability to record, process, summarize and
report financial information; and
 
 b)  Any
fraud, whether or not material, that involves management or other employees who
have a significant role in the registrant’s internal control over financial
reporting.
 
 March 2,
2005
 /s/
James R. Gibbs
 James R.
Gibbs
 Chairman
of the Board, President
 and Chief
Executive Officer