Exhibit 5.1

May 20, 2020

National Oilwell Varco, Inc.

7909 Parkwood Circle Drive

Houston, Texas 77036

Ladies and Gentlemen:

We have acted as counsel to National Oilwell Varco, Inc., a Delaware corporation (the “Company”), in connection with the proposed issuance of up to an additional 22,500,000 shares of common stock, $0.01 par value per share (the “Shares”), pursuant to a registration statement on Form S-8 (the “Registration Statement”) under the Securities Act of 1933, as amended (the “Act”), to be filed with the U.S. Securities and Exchange Commission (the “Commission”), which Shares are issuable under the National Oilwell Varco, Inc. 2018 Long-Term Incentive Plan (the “Plan”).

This opinion letter is delivered in accordance with the requirements of Item 601(b)(5) of Regulation S-K promulgated under the Act.

As the basis for the opinion hereinafter expressed, we have examined: (i) originals, or copies certified or otherwise identified to us as being true and complete copies of the originals, of (a) the Plan; (b) the Fifth Amended and Restated Certificate of Incorporation of the Company, as amended to date; (c) the Amended and Restated Bylaws of the Company; (d) certain resolutions of the Board of Directors of the Company; and (e) such other corporate records, certificates, instruments and documents as we have deemed necessary or advisable for the purposes of this opinion; and (ii) such statutes, including the Delaware General Corporation Law (the “DGCL”), and regulations as we have deemed necessary or advisable for the purposes of this opinion.

In our examination, we have assumed the legal capacity of all natural persons, the genuineness of all signatures, the authenticity of all documents submitted to us as certified or photostatic copies and the authenticity of the originals of such latter documents. As to any facts material to this opinion that we did not independently establish or verify, we have relied upon oral or written statements and representations of officers and other representatives of the Company and others.

Based upon the foregoing and subject to the assumptions, qualifications and limitations set forth herein, we are of the opinion that the Shares have been duly authorized and, when issued, paid for and delivered pursuant to the terms and in the manner set forth in the Plan, and assuming that the Shares have been and remain duly reserved for issuance within the limits of the common stock then remaining authorized but unissued, the Shares will be validly issued, fully paid and nonassessable.

The foregoing opinion is based upon and limited to the DGCL (including the statutory provisions, the applicable provisions of the Delaware Constitution and reported judicial decisions interpreting the foregoing). We express no opinion herein as to any other laws, statutes, regulations or ordinances. This opinion is given as of the date hereof and we assume no obligation to update or supplement such opinion to reflect any facts or circumstances that may hereafter come to our attention or any changes that may hereafter occur. This opinion letter is being furnished solely for the Company’s benefit in connection with the offer, sale and issuance of the Shares and is not to be used, quoted or otherwise referred to for any other purpose without our prior written consent.

We hereby consent to the filing of this opinion letter as Exhibit 5.1 to the Registration Statement. In giving such consent, we do not thereby concede that we are experts within the meaning of the Act or that our firm is within the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Commission.

Very truly yours,

/s/ Winston & Strawn LLP