UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

SCHEDULE 13D

Under the Securities Exchange Act of 1934

(Amendment No. )*

Culp, Inc.

(Name of Issuer)

Common Stock, par value $0.05 per share

(Title of Class of Securities)

230215105

(CUSIP Number)

Mill Road Capital III, L.P.

Attn: Thomas E. Lynch

382 Greenwich Avenue

Suite One

Greenwich, CT 06830

203-987-3500

With a copy to:

Peter M. Rosenblum, Esq.

Foley Hoag LLP

155 Seaport Blvd.

Boston, MA 02210

617-832-1000

(Name, Address and Telephone Number of Person Authorized to Receive Notices and Communications)

December 9, 2022

(Date of Event which Requires Filing of this Statement)

If the filing person has previously filed a statement on Schedule 13G to report the acquisition that is the subject of this Schedule 13D, and is filing this schedule because of §§240.13d-1(e), 240.13d-1(f) or 240.13d-1(g), check the following box. [X]

Note: Schedules filed in paper format shall include a signed original and five copies of the schedule, including all exhibits. See §240.13d-7 for other parties to whom copies are sent.

The information required on the remainder of this cover page shall not be deemed to be “filed” for the purpose of Section 18 of the Securities Exchange Act of 1934 (“Act”) or otherwise subject to the liabilities of that section of the Act but shall be subject to all other provisions of the Act (however, see the Notes).

This joint statement on Schedule 13D relates to the common stock, par value $0.05 per share (the “Common Stock”), of Culp, Inc., a North Carolina corporation (the “Issuer”). The address of the Issuer’s principal executive offices is 1823 Eastchester Drive, High Point, North Carolina 27265.

(a) This joint statement on Schedule 13D is being filed by Thomas E. Lynch, Mill Road Capital III GP LLC, a Cayman Islands limited liability company (the “GP”), and Mill Road Capital III, L.P., a Cayman Islands exempted limited partnership (the “Fund”). Each of the foregoing is referred to in this Schedule 13D as a “Reporting Person” and, collectively, as the “Reporting Persons.” Mr. Lynch, Justin C. Jacobs, Deven Petito and Eric Yanagi are the management committee directors of the GP and, in this capacity, are referred to in this Schedule 13D as the “Managers.” The GP is the sole general partner of the Fund. Mr. Lynch has shared authority to vote and dispose of the shares of Common Stock reported in this Schedule 13D.

The Reporting Persons have entered into a Joint Filing Agreement dated July 6, 2020, a copy of which is filed as Exhibit 1 to this Schedule 13D, pursuant to which they have agreed to file this Schedule 13D jointly in accordance with Rule 13d-1(k) under the Securities Exchange Act of 1934, as amended (the “Exchange Act”).

(b) The business address of Mr. Lynch and Mr. Petito, and the address of the principal business and the principal office of the Fund and the GP is 382 Greenwich Avenue, Suite One, Greenwich, CT 06830. The business address of Mr. Jacobs is 7448 NE 4th Court, Miami, FL 33138. The business address of Mr. Yanagi is 400 Oyster Point Blvd, Suite 526, South San Francisco, CA 94080.

(c) The principal business of the GP is acting as the sole general partner of the Fund. The principal business of the Fund is investing in securities. The present principal occupation or employment of each Manager is as a management committee director of the GP and Mill Road Capital Management LLC, a Delaware limited liability company (the “Management Company”), which provides advisory and administrative services to the GP and is located at 382 Greenwich Avenue, Suite One, Greenwich, Connecticut 06830.

(d) None of the Managers, the GP and the Fund has, during the last five years, been convicted in a criminal proceeding (excluding traffic violations or similar misdemeanors).

(e) None of the Managers, the GP and the Fund was, during the last five years, a party to a civil proceeding of a judicial or administrative body of competent jurisdiction and, as a result of such proceeding, was or is subject to a judgment, decree or final order (1) enjoining future violations of, or prohibiting or mandating activities subject to, federal or state securities laws, or (2) finding any violation with respect to such laws.

(f) Each Manager is a citizen of the United States.

The Reporting Persons acquired beneficial ownership of an aggregate of 695,469 shares of Common Stock for $6,273,490 using working capital from the Fund and the proceeds of margin loans under margin loan facilities maintained in the ordinary course of business by the Fund with a broker on customary terms and conditions.

The Reporting Persons acquired shares of the Common Stock in the Reporting Persons’ ordinary course of business based on their belief that the Common Stock represents an attractive investment opportunity.

The Reporting Persons intend to review continuously their equity interest in the Issuer. Depending upon their evaluation of the factors described below, one or more of the Reporting Persons may from time to time purchase additional securities of the Issuer, dispose of all or a portion of the securities then held by such Reporting Persons, or cease buying or selling such securities; any such additional purchases or sales of securities of the Issuer may be in the open market, in privately negotiated transactions or otherwise.

The Reporting Persons may wish to engage in a constructive dialogue with officers, directors and other representatives of the Issuer, as well as the Issuer’s shareholders; topics of discussion may include, but are not limited to, the Issuer’s markets, operations, competitors, prospects, strategy, personnel, directors, ownership and capitalization. The Reporting Persons may also enter into confidentiality or similar agreements with the Issuer and, subject to such an agreement or otherwise, exchange information with the Issuer. The factors that the Reporting Persons may consider in evaluating their equity interest in the Issuer’s business include the following: (i) the Issuer’s business and prospects; (ii) the performance of the Common Stock and the availability of the Common Stock for purchase at particular price levels; (iii) the availability and nature of opportunities to dispose of the Reporting Persons’ interests; (iv) general economic conditions; (v) stock market conditions; (vi) other business and investment opportunities available to the Reporting Persons; and (vii) other plans and requirements of the Reporting Persons.

Depending on their assessment of the foregoing factors, the Reporting Persons may, from time to time, modify their present intention as stated in this Item 4.

The Reporting Persons intend to continuously review their options but, except as set forth above, do not have at this time any other specific plans that would result in (a) the acquisition of additional securities of the Issuer or the disposition of securities of the Issuer; (b) any extraordinary corporate transactions such as a merger, reorganization or liquidation involving the Issuer or any of its subsidiaries; (c) any sale or transfer of a material amount of the assets of the Issuer or of any of its subsidiaries; (d) any change in the present management or Board of Directors of the Issuer, including any plans or proposals to change the number or term of directors or to fill any existing vacancies on the Issuer’s Board of Directors; (e) any material change in the present capitalization or dividend policy of the Issuer; (f) any other material change in the Issuer’s business or corporate structure; (g) any change in the Issuer’s charter or by-laws that may impede the acquisition of control of the Issuer by any person; (h) the Issuer’s

Common Stock being delisted from a national securities exchange or ceasing to be authorized to be quoted in an inter-dealer quotation system or a registered national securities association; (i) causing a class of equity securities of the Issuer to become eligible for termination of registration pursuant to Section 12(g)(4) of the Securities Exchange Act of 1934, as amended; or (j) any action similar to those enumerated above.

(a, b) The percentages of beneficial ownership reported in this Item 5, and on each Reporting Person’s cover page to this Schedule 13D, are based on a total of 12,293,762 shares of Common Stock issued and outstanding as of December 7, 2022, as reported in the Issuer’s quarterly report on Form 10-Q for the fiscal quarter ended October 30, 2022. All of the share numbers reported below, and on each Reporting Person’s cover page to this Schedule 13D, are as of December 13, 2022, unless otherwise indicated. The cover page to this Schedule 13D for each Reporting Person is incorporated by reference in its entirety into this Item 5(a, b).

The Fund directly holds, and thus has sole voting and dispositive power over, 695,469 shares of Common Stock. The GP, as sole general partner of the Fund, also has sole authority to vote (or direct the vote of), and to dispose (or direct the disposal) of, these shares on behalf of the Fund, and Mr. Lynch has shared authority to vote (or direct the vote of), and to dispose (or direct the disposal) of, these shares on behalf of the GP. Accordingly, each of the Reporting Persons beneficially owns 695,469 shares of Common Stock, or approximately 5.7% of the outstanding shares of Common Stock, and the Reporting Persons beneficially own, in the aggregate, 695,469 shares of Common Stock, or approximately 5.7% of the outstanding shares of Common Stock.

(c) No Reporting Person effected any transaction in shares of the Common Stock from October 14, 2022 (the date 60 days prior to the filing of this Schedule 13D) to December 13, 2022.

(d) No person other than the Reporting Persons is known to have the right to receive or the power to direct the receipt of dividends from or the proceeds from the sale of shares of the Common Stock.

(e) Not applicable.

Except as otherwise described in this Schedule 13D, including the Exhibits attached hereto, there are no contracts, arrangements, understandings, or relationships (legal or otherwise) among the Reporting Persons, or between any Reporting Person(s) and any third party, with respect to any securities of the Issuer, including, but not limited to, those involving the transfer or voting of any of the securities, finder’s fees, joint ventures, loan or option arrangements, put or calls, guarantees of profits, division of profits or losses, or the giving or withholding of proxies.

[signature pages follow]

Signature

After reasonable inquiry and to the best of my knowledge and belief, I certify that the information set forth in this statement is true, complete and correct.