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Exhibit 23.1 Consent of Independent Registered Public Accounting Firm The Board of Directors and Stockholders
America West Holdings Corporation: We consent to the incorporation by reference in the registration statements on Form S-3 (No.
333-113471, No. 333-110031 and No. 333-88588) of America West Holdings Corporation (the Company)
and America West Airlines, Inc., (AWA) the registration statement on Form S-3 (No. 333-02129) of
AWA and the registration statements on Form S-8 (No. 333-118188, No. 333-94361, No. 333-40486 and
No. 333-89288) of the Company of our reports dated March 11, 2005, with respect to the consolidated
balance sheets of the Company and subsidiary as of December 31, 2004 and 2003, and the related
consolidated statements of operations, cash flows and stockholders equity and comprehensive income
for the years then ended, the related consolidated financial statement schedule, and our report on
managements assessment of the effectiveness of internal control over financial reporting and the
effectiveness of internal control over financial reporting as of December 31, 2004, which reports
appear in the December 31, 2004 annual report on Form 10-K of the Company. Our report on
managements assessment of the effectiveness of internal control over financial reporting and the
effectiveness of internal control over financial reporting as of December 31, 2004 expresses our
opinion that the Company did not maintain effective internal control over financial reporting as of
December 31, 2004 because of the effect of a material weakness on the achievement of the objectives
of the control criteria and contains an explanatory paragraph that states the Company did not
maintain effective internal control over financial reporting due to a material weakness associated
with its accounting for AWAs fuel hedging transactions. Management concluded that AWAs fuel
hedging transactions did not qualify for hedge accounting under U.S. generally accepted accounting
principles and that the Companys financial statements for prior periods required restatement to
reflect the fair value of fuel hedging contracts in the balance sheets and statements of
stockholders equity and comprehensive income for Holdings and AWA. These accounting errors were
the result of deficiencies in its internal control over financial reporting from the lack of
effective reviews of hedge transaction documentation and of quarterly mark-to-market accounting
entries on open fuel hedging contracts by personnel at an appropriate level. We also consent to the incorporation by reference of our reports dated March 11, 2005, relating to
the consolidated balance sheets of AWA and subsidiary as of December 31, 2004 and 2003, and the
related consolidated statements of operations, cash flows and stockholders equity and
comprehensive income for the years then ended, and the related financial statement schedule, which
reports appear in the December 31, 2004 annual report on Form 10-K of AWA. Our report dated March 11, 2005, related to the consolidated financial statements of the Company
refers to the restatement of the Companys consolidated balance sheet and consolidated statement of
stockholders equity as of and for the year ended December 31, 2003 and the restatement of the
Companys dilutive earnings per share for the year ended December 31, 2003 in connection with the
adoption of Emerging Issues Task Force 04-8 The Effect of Contingently Convertible Instruments on
Diluted Earnings Per Share. Our report dated March 11, 2005, related to the consolidated
financial statements of AWA refers to the restatement of AWAs consolidated balance sheet and
consolidated statement of stockholders equity as of and for the year ended December 31, 2003. /s/ KPMG LLP Phoenix, Arizona
March 11, 2005