EXHIBIT 24

                               POWER OF ATTORNEY

Know all by these presents, that the undersigned hereby constitutes and
appoints each of John L. Howard, Laurence M. Trusdell and Aimee Nolan, signing
singly, the undersigned's true and lawful attorney-in-fact to:

(1) execute for and on behalf of the undersigned Forms 3, 4, 5, and 144
relating to equity securities of W.W. Grainger, Inc. (the "Company") in
accordance with Section 16(a) of the Securities Exchange Act of 1934 and the
rules thereunder and Rule 144 under the Securities Act of 1933;

(2) do and perform any and all acts for and on behalf of the undersigned which
may be necessary or desirable to complete any such Form 3, 4, 5, or 144 and
timely file the same with the United States Securities and Exchange Commission
and any stock exchange or similar authority; and

(3) take any other action of any type whatsoever in connection with the
foregoing which, in the opinion of the attorney-in-fact, may be of benefit to,
in the best interest of, or legally required by, the undersigned, it being
understood that the documents executed by the attorney-in-fact on behalf of the
undersigned pursuant to this Power of Attorney shall be in such form and shall
contain such terms and conditions as the attorney-in-fact may approve in his
or her discretion.

The undersigned hereby grants to each attorney-in-fact full power and authority
to do and perform any and every act and thing whatsoever requisite, necessary
or proper to be done in the exercise of any of the rights and powers herein
granted, as fully to all intents and purposes as the attorney-in-fact might or
could do if personally present, with full power of substitution or revocation,
hereby ratifying and confirming all that the attorney-in-fact, or his or her
substitute or substitutes, shall lawfully do or cause to be done by virtue of
this Power of Attorney and the rights and powers herein granted.

The undersigned acknowledges that the attorneys-in-fact, in serving in such
capacity at the request of the undersigned, are not assuming, nor is the Company
assuming, any of the undersigned's responsibilities to comply with Section 16
of the Securities Exchange Act of 1934 or Rule 144 under the Securities Act
of 1933.

This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file Forms 3, 4, 5, and 144 with respect
to the undersigned's holdings of and transactions in equity securities of the
Company, unless earlier revoked by the undersigned in a signed writing
delivered to the attorneys-in-fact.

IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to be
executed as of the 22nd day of July, 2004.

/s/ H. B. Smith
H. B. Smith