EXHIBIT 23.1

Consent of Independent Registered Public Accounting Firm

We hereby consent to the incorporation by reference of our reports, dated March 15, 2005 relating to our audits of the consolidated financial statements, the financial statement schedule and internal control over financial reporting, appearing in this Annual Report on Form 10-K of Maxwell Technologies, Inc. for the year ended December 31, 2004 in the previously filed Registration Statements of Maxwell Technologies, Inc. on Form S-8 (File Nos. 333-86686, 333-86688, 333-53278, 033-88634, 333-41632, 333-41634, 333-41670, 333-28459, 333-07831 and 033-88638) and on Form S-3 (File No. 333-118849).

/s/    MCGLADREY & PULLEN, LLP

San Diego, California

March 18, 2005