<PAGE>

                                                                Exhibit 31.1

                                CERTIFICATION
                                -------------

I, Mark E. Schwarzmann, certify that:

1. I have reviewed this quarterly report on Form 10-Q of IDS Life Insurance
   Company;

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 officer(s) 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)) 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) 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

   (c) 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 officer(s) 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.



   Date: May 5, 2005                           /s/ Mark E. Schwarzmann
                                               -----------------------------
                                               Mark E. Schwarzmann
                                               Chief Executive Officer