Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We have issued our reports dated March 5, 2021, with respect to the consolidated financial statements and internal control over financial reporting included in the Annual Report of Covenant Logistics Group, Inc. on Form 10-K for the year ended December 31, 2020. We consent to the incorporation by reference of said reports in the Registration Statements of Covenant Logistics Group, Inc. on Form S-3 (File No. 333-228425) and Forms S-8 (File No. 333-2654, File No. 033-88686, File No. 333-67559, File No. 333-37356, File No. 333-50174 , File No. 333-88486, File No. 333-105880, File No. 333-134939, File No. 333-174582, File No. 333-189060, File No. 333-231390 and File No. 333-239724).

/s/ Grant Thornton LLP

Atlanta, GA

March 5, 2021