Exhibit (a)(5)(ii)

This announcement is neither an offer to purchase nor a solicitation of an offer to sell shares of Class A common stock of Covenant Logistics Group, Inc. The Offer (as defined below) is made solely by the Offer to Purchase, dated August 9, 2021, and the related Letter of Transmittal, and any amendments or supplements thereto. The Offer is not being made to, nor will tenders be accepted from or on behalf of holders of shares of Class A common stock in any jurisdiction in which the making or acceptance of offers to sell shares of Class A common stock would not be in compliance with the laws of that jurisdiction. In any jurisdiction where the securities, blue sky, or other laws require the Offer to be made by a licensed broker or dealer, the Offer shall be deemed made on behalf of Covenant Logistics Group, Inc. by one or more brokers or dealers registered under the laws of such jurisdiction.

Notice of Offer to Purchase

by

Covenant Logistics Group, Inc.

Up to $40.0 Million in Value of Shares of its Class A Common Stock

At a Cash Purchase Price Not Greater than $23.00 per Share Nor Less than $21.00 per Share

Covenant Logistics Group, Inc., a Nevada corporation (the “Company”), is offering to purchase up to $40.0 million in value of shares of its Class A common stock, $0.01 par value per share (the “Shares”), at a price not greater than $23.00 nor less than $21.00per Share, to the seller in cash, less any applicable withholding taxes and without interest, upon the terms and subject to the conditions described in the Offer to Purchase, dated August 9, 2021 (the “Offer to Purchase”), and the related Letter of Transmittal (the “Letter of Transmittal”) (which together, as they may be amended and supplemented from time to time, constitute the “Offer”).

THE OFFER, PRORATION PERIOD, AND WITHDRAWAL RIGHTS WILL EXPIRE AT ONE MINUTE AFTER 11:59 P.M., NEW YORK CITY TIME, ON SEPTEMBER 3, 2021, UNLESS THE OFFER IS EXTENDED (SUCH DATE AND TIME, AS THEY MAY BE EXTENDED, THE “EXPIRATION DATE”).

The Offer is not conditioned on the receipt of financing or any minimum number of Shares being tendered. The Offer is, however, subject to other conditions as set forth in the Offer to Purchase.

Upon the terms and subject to the conditions of the Offer, which will be conducted through a modified “Dutch auction” process, the Company will determine a single per Share purchase price, not greater than $23.00 nor less than $21.00per Share, to the seller in cash, less any applicable withholding taxes and without interest, that the Company will pay for Shares properly tendered and not properly withdrawn in the Offer, taking into account the total number of Shares tendered and the prices specified, or deemed specified, by tendering stockholders. The Company will select the single lowest purchase price (in multiples of $0.25) within the price range specified above that will allow it to purchase up to $40.0 million in value of Shares. Upon the terms and subject to the conditions of the Offer, if, based on the purchase price determined by the Company, Shares having an aggregate value of less than $40.0 million are properly tendered and not properly withdrawn, the Company will select the lowest price that will allow the Company to buy all the Shares that are properly tendered and not properly withdrawn before the Offer expires. All Shares the Company purchases in the Offer will be acquired at the same purchase price regardless of whether any stockholder tenders at a lower price. Only Shares properly tendered at prices at or below the purchase price selected by the Company and not properly withdrawn will be purchased. However, because of proration, “Odd Lot” priority, and conditional tender provisions described in the Offer to Purchase, the Company may not purchase all of the Shares tendered at or below the purchase price if, based on the purchase price determined by the Company, more than $40.0 million in value of Shares are properly tendered and not properly withdrawn. If any properly tendered Shares are not purchased under the Offer or are properly withdrawn before the Expiration Date, or if less than all Shares evidenced by a stockholder’s certificate(s) are tendered, the Company will credit the certificates to book-entry for unpurchased Shares promptly after the expiration or termination of the Offer.

The Company reserves the right, in its sole discretion, to change the per Share purchase price range and to increase or decrease the value of Shares sought in the Offer, subject to applicable law. In accordance with the rules of the Securities and Exchange Commission, the Company may increase the number of Shares accepted for payment in the Offer by no more than 2% of the outstanding Shares without extending the Offer.

As of August 5, 2021, there were 14,453,675 Shares outstanding. At the maximum Final Purchase Price (as defined in the Offer to Purchase) of $23.00 per Share, the Company could purchase 1,739,130 Shares if the Offer is fully subscribed, which would represent approximately 12.0% of the outstanding Shares as of August 5, 2021. At the minimum Final Purchase Price of $21.00 per Share, the Company could purchase 1,904,761 Shares if the Offer is fully subscribed, which would represent approximately 13.2% of the outstanding Shares as of August 5, 2021. The Shares are listed and traded on the NASDAQ Global Select Market under the symbol “CVLG.” The Offer does not cover the Company’s Class B common stock, of which there are 2,350,000 shares outstanding. Stockholders are urged to obtain current market quotations for the Shares before deciding whether and at what purchase price or purchase prices to tender their Shares.

The Company expressly reserves the right, in its sole discretion, at any time and from time to time, to extend the period of time during which the Offer is open and thereby delay acceptance for payment of, and payment for, any Shares by giving oral or written notice of such extension to Computershare Trust Company N.A., the depositary for the Offer (the “Depositary”), and making a public announcement of such extension not later than 9:00 a.m., New York City time, on the first business day after the previously scheduled Expiration Date.

The Offer will expire at one minute after 11:59 p.m., New York City time, on Friday, September 3, 2021, unless the Company exercises its right, in its sole discretion, to extend the period of time during which the Offer will remain open. Beneficial owners should be aware that their broker, dealer, commercial bank, trust company or other nominee may establish its own earlier deadlines for participation in the Offer. Accordingly, beneficial owners wishing to participate in the Offer should contact their broker, dealer, commercial bank, trust company or other nominee as soon as possible in order to determine the times by which such owner must take action in order to participate in the Offer.

In accordance with the instructions to the Letter of Transmittal, stockholders wishing to tender Shares must specify the price or prices, not greater than $23.00 nor less than $21.00 per Share, at which they are willing to sell their Shares to the Company in the Offer. Alternatively, each stockholder desiring to tender Shares can choose not to specify a price and, instead, elect to tender their Shares at the purchase price ultimately paid for Shares properly tendered and not properly withdrawn in the Offer. If a stockholder agrees to accept the purchase price determined in the Offer, its Shares will be deemed to be tendered at the minimum price of $21.00per Share, which could result in the tendering stockholder receiving the minimum price of $21.00per Share. See the Offer to Purchase for recent market prices for the Shares.

Stockholders wishing to tender Shares must follow the procedures set forth in the Offer to Purchase and in the related Letter of Transmittal. Generally, for Shares to be properly tendered pursuant to the Offer, the certificates for such Shares (or confirmation of receipt of such Shares pursuant to the procedure for book-entry transfer set forth in the Offer to Purchase), together with a properly completed and duly executed Letter of Transmittal, including any required signature guarantees, or an Agent’s Message (as defined in the Offer to Purchase), and any other documents required by the Letter of Transmittal, must be received before one minute after 11:59 p.m., New York City time, on Friday, September 3, 2021 (or the earlier deadline with respect to Shares held within the 401(k) Plan (as defined in the Offer to Purchase)) by the Depositary at one of its addresses set forth on the back cover of the Offer to Purchase.

Upon the terms and subject to the conditions of the Offer, if, based on the purchase price determined by the Company, Shares having an aggregate value in excess of $40.0 million (or such greater amount as the Company may elect to pay, subject to applicable law) are properly tendered at or below the purchase price and not properly withdrawn prior to the Expiration Date, the Company will purchase Shares as follows:

• first, all Odd Lots (as defined in the Offer to Purchase) of less than 100 Shares at the Final Purchase Price from stockholders who properly tender all of their Shares at or below the Final Purchase Price and who do not properly withdraw them before the Expiration Date (tenders of less than all of the Shares owned, beneficially or of record, by such Odd Lot Holder (as defined in the Offer to Purchase) will not qualify for this preference);

• second, after purchasing all the Odd Lots that were validly tendered at or below the Final Purchase Price, subject to the conditional tender provisions (whereby a holder may specify a minimum number of such holder’s Shares that must be purchased if any such Shares are purchased), the Company will purchase all Shares properly tendered at or below the Final Purchase Price on a pro rata basis with appropriate adjustment to avoid purchases of fractional Shares; and

• third, only if necessary to permit the Company to purchase $40.0 million in value of Shares (or such greater amount as the Company may elect to pay, subject to applicable law), the Company will purchase Shares conditionally tendered (for which the condition was not initially satisfied) at or below the Final Purchase Price, by random lot, to the extent feasible. To be eligible for purchase by random lot, stockholders whose Shares are conditionally tendered must have tendered all of their Shares. Random lot selection would be facilitated by the Company.

For purposes of the Offer, the Company will be deemed to have accepted for payment (and therefore purchased), subject to proration, and conditional tender provisions of the Offer, Shares that are properly tendered at or below the purchase price selected by the Company and not properly withdrawn only when, as and if the Company gives oral or written notice to the Depositary of the Company’s acceptance of the Shares for payment pursuant to the Offer.

Upon the terms and subject to the conditions of the Offer, the Company will accept for payment and pay the per Share purchase price for all of the Shares accepted for payment pursuant to the Offer promptly after the Expiration Date. In all cases, payment for Shares tendered and accepted for payment pursuant to the Offer will be made promptly, subject to possible delay in the event of proration, but only after timely receipt by the Depositary of: (i) certificates for Shares or a timely book-entry confirmation of the deposit of Shares into the Depositary’s account at the Book-Entry Transfer Facility (as defined in the Offer to Purchase); (ii) a properly completed and duly executed Letter of Transmittal, including any required signature guarantee (or, in the case of a book-entry transfer, an Agent’s Message (as defined in the Offer to Purchase)); and (iii) any other required documents.

Because of the difficulty in determining the number of Shares properly tendered and not properly withdrawn, and because of the proration and conditional tender provisions described in the Offer to Purchase, the Company expects that it will not be able to announce the final proration factor or commence payment for any Shares purchased pursuant to the Offer until after the Expiration Date. The preliminary results of any proration will be announced by press release as promptly as practicable after the Expiration Date.

Tenders of Shares are irrevocable, except that such Shares may be withdrawn at any time prior to the Expiration Date and, unless such Shares have been accepted for payment as provided in the Offer, stockholders may also withdraw their previously tendered Shares at any time after one minute after 11:59 p.m., New York City time, on September 3, 2021. For a withdrawal to be effective, a written notice of withdrawal must be received in a timely manner by the Depositary at one of its addresses listed on the back cover of the Offer to Purchase. Any such notice of withdrawal must specify the name of the person having tendered the Shares to be withdrawn, the number of Shares to be withdrawn and the name of the registered holder of the Shares to be withdrawn, if different from the name of the person who tendered the Shares. If certificates for Shares have been delivered or otherwise identified to the Depositary, then, prior to the physical release of those certificates, the serial numbers shown on those certificates must be submitted to the Depositary and, unless an Eligible Institution (as defined in the Offer to Purchase) has tendered those Shares, an Eligible Institution must guarantee the signatures on the notice of withdrawal. If a stockholder has used more than one Letter of Transmittal or has otherwise tendered Shares in more than one group of Shares, the stockholder may withdraw Shares using either separate notices of withdrawal or a combined notice of withdrawal, so long as the information specified above is included. If Shares have been delivered in accordance with the procedures for book-entry transfer described in the Offer to Purchase, any notice of withdrawal must also specify the name and number of the account at the Book-Entry Transfer Facility to be credited with the withdrawn Shares and otherwise comply with the Book-Entry Transfer Facility’s procedures.

The Company will decide, in its sole discretion, all questions as to the form and validity, including time of receipt, of notices of withdrawal, and each such decision will be final and binding on all parties absent a finding to the contrary by a court of competent jurisdiction. None of the Company, its Board of Directors, Computershare Trust Company, N.A., as the Depositary, Georgeson LLC, as the information agent (the “Information Agent”), or any other person will be under any duty to give notification of any defects or irregularities in any notice of withdrawal or incur any liability for failure to give any such notification.

Based on our confidence in the long-term outlook for our business, and consistent with our balanced approach to capital allocation, we have determined to use up to $40.0 million of a combination of existing cash resources and borrowings to repurchase Shares in the Offer. The Offer is not subject to a financing condition.

The Company is making the Offer because we believe that the modified Dutch auction tender offer set forth in the Offer to Purchase represents an efficient mechanism to provide all of the Company’s stockholders with the opportunity to tender all or a portion of their Shares and, thereby, receive a return of some or all of their investment if they so elect. In addition, if the Company completes the Offer, stockholders who do not participate in the Offer will automatically increase their relative percentage ownership interest in the Company and its future operations.

The Offer also provides stockholders with an efficient way to sell their Shares without incurring broker’s fees or commissions associated with open market sales.

Generally, if you are a U.S. Holder (as defined in the Offer to Purchase), your receipt of cash from us in exchange for the Shares you tender will be a taxable transaction for United States federal income tax purposes. The cash you receive for your tendered Shares will generally be treated for United States federal income tax purposes either as consideration received in respect of a sale or exchange of the Shares purchased by us or as a distribution from us in respect of Shares. We urge you to consult your own tax advisor as to the particular tax consequences to you of the Offer. If you are a non-U.S. Holder (as defined in the Offer to Purchase), because it is unclear whether the cash you receive in connection with the Offer will be treated (i) as proceeds of a sale or exchange or (ii) as a distribution, the Depositary or other applicable withholding agent may treat such payment as a dividend distribution for withholding purposes. Accordingly, if you are a non-U.S. Holder, you may be subject to withholding on payments to you at a rate of 30% of the gross proceeds paid, unless you establish an entitlement to a reduced rate of withholding by timely completing, under penalties of perjury, the applicable Form W-8. Non-U.S. Holders are urged to consult their tax advisors regarding the application of United States federal income tax withholding and backup withholding, including eligibility for a withholding tax reduction or exemption and the refund procedure. All stockholders should read carefully the Offer to Purchase, in particular, Section 3, Section 6, and Section 13, for additional information regarding the United States federal income tax consequences of participating in the Offer and should consult their financial and tax advisors.

The Company’s Board of Directors has authorized us to make the Offer. However, none of the Company, the members of its Board of Directors, the Depositary, or the Information Agent makes any recommendation to any stockholder as to whether to tender or refrain from tendering any Shares or as to the price or prices at which stockholders may choose to tender their Shares. None of the Company, the members of its Board of Directors, the Depositary, or the Information Agent has authorized any person to make any recommendation with respect to the Offer. Stockholders should carefully evaluate all information in the Offer to Purchase and in the related Letter of Transmittal and should consult their own financial and tax advisors. Stockholders must decide whether to tender their Shares and, if so, how many Shares to tender and the price or prices at which a stockholder will tender. In doing so, a stockholder should read carefully the information in the Offer to Purchase and in the related Letter of Transmittal before making any decision with respect to the Offer.

The information required to be disclosed by Rule 13e-4(d)(1) of the Securities Exchange Act of 1934, as amended, is contained in the Offer to Purchase and is incorporated herein by reference. The Company is also filing with the Securities and Exchange Commission an Issuer Tender Offer Statement on Schedule TO, which includes certain additional information relating to the Offer.

Copies of the Offer to Purchase and the related Letter of Transmittal are being mailed to all holders of the Shares, including brokers, dealers, commercial banks and trust companies whose names, or the names of whose nominees, appear on the Company’s stockholder list or, if applicable, who are listed as participants in a clearing agency’s security position listing for subsequent transmittal to beneficial owners of Shares, as reflected on the records of the transfer agent. The Offer is explained in detail in those materials.

Questions or requests for assistance may be directed to the Information Agent, at their address and telephone number set forth below. Copies of the Offer to Purchase, the Letter of Transmittal and other related materials will be furnished promptly by the Information Agent at the Company’s expense. Stockholders may also contact their broker, dealer, commercial bank, trust company or other nominee for assistance concerning the Offer.

The Information Agent for the Offer is:

Georgeson LLC

1290 Avenue of the Americas, 9^th Floor

New York, New York 10104

Banks, Brokers, and Stockholders Call Toll-Free: (888) 607-9107

August 9, 2021

Schedule to TO-I