Exhibit 5.1

W.W. Grainger, Inc.

100 Grainger Parkway

Lake Forest, Illinois 60045

Re: W.W. Grainger, Inc. Registration Statement on Form S-3

Ladies and Gentlemen:

We have acted as special counsel to W.W. Grainger Inc., an Illinois corporation (the “Company”), in connection with the offer and sale of $400,000,000 aggregate principal amount of 4.20% Senior Notes due 2047 (the “Securities”) as set forth in the Prospectus Supplement dated May 15, 2017 (the “Prospectus Supplement”) as filed with the Securities and Exchange Commission pursuant to Rule 424(b)(5) under the Securities Act of 1933, as amended.

The Securities will be issued under an Indenture, dated as of June 11, 2015, between the Company and U.S. Bank National Association as Trustee (the “Trustee”) as supplemented by the Third Supplemental Indenture, dated as of May 22, 2017, between the Company and the Trustee (collectively, the “Indenture”).

As special counsel to the Company, we have examined originals or copies certified or otherwise identified to our satisfaction of the Company’s Restated Articles of Incorporation, the Company’s Bylaws, resolutions of the Company’s Board of Directors and such Company records, certificates and other documents and such questions of law as we considered necessary or appropriate for the purpose of this opinion. In rendering this opinion, we have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as originals and the conformity to authentic original documents of all documents submitted to us as copies.

Based upon and subject to the foregoing and to the assumptions, conditions and limitations set forth herein, we are of the opinion that upon the due execution, authentication, issuance and delivery of the Securities, and the receipt of the consideration therefor set forth in the Prospectus Supplement, the Securities will be valid and binding obligations of the Company entitled to the benefits of the Indenture and enforceable against the Company in accordance with their terms, except as such enforceability may be limited by bankruptcy, insolvency, fraudulent conveyance, moratorium, reorganization or similar laws affecting creditors’ rights generally and subject to general principles of equity.

Mayer Brown LLP operates in combination with other Mayer Brown entities with offices in Europe and Asia and is associated with Tauil & Chequer Advogados, a Brazilian law partnership.

We hereby consent to the filing of this opinion as an exhibit to the Company’s Current Report on Form 8-K and to being named in the Prospectus Supplement under the caption “Legal Matters” with respect to the matters stated therein.