EXHIBIT 23.1 Consent of Independent Auditor We consent to the incorporation by reference in the Registration Statement (Form S-8 No. 33-44139) pertaining to the 1991 Employee Stock Option Plan of Old Dominion Freight Line, Inc. of our report dated January 24, 2001, except for the information presented in Note 2 and Note 8, for which the date is February 1, 2001, with respect to the consolidated financial statements and schedule of Old Dominion Freight Line, Inc. included in the Annual Report (Form 10-K) for the year ended December 31, 2000. Ernst & Young LLP Winston-Salem, North Carolina March 14, 2001 36