Statement of Changes in Beneficial Ownership (4)

FORM 4 [ ] Check this box if no longer subject to Section 16. Form 4 or Form 5 obligations may continue. See Instruction 1(b).	UNITED STATES SECURITIES AND EXCHANGE COMMISSION Washington, D.C. 20549 STATEMENT OF CHANGES IN BENEFICIAL OWNERSHIP OF SECURITIES	OMB APPROVAL OMB Number: 3235-0287 Estimated average burden hours per response... 0.5
	Filed pursuant to Section 16(a) of the Securities Exchange Act of 1934 or Section 30(h) of the Investment Company Act of 1940

1. Name and Address of Reporting Person * Robbins Paige K	2. Issuer Name and Ticker or Trading Symbol GRAINGER W W INC [ GWW ]	5. Relationship of Reporting Person(s) to Issuer (Check all applicable) _____ Director                      _____ 10% Owner __ X __ Officer (give title below)      _____ Other (specify below) Sr. VP, Chief Digital Officer
(Last)          (First)          (Middle) 100 GRAINGER PARKWAY	3. Date of Earliest Transaction (MM/DD/YYYY) 4/2/2018
(Street) LAKE FOREST, IL 60045 (City)        (State)        (Zip)	4. If Amendment, Date Original Filed (MM/DD/YYYY)	6. Individual or Joint/Group Filing (Check Applicable Line) _ X _ Form filed by One Reporting Person ___ Form filed by More than One Reporting Person

Table I - Non-Derivative Securities Acquired, Disposed of, or Beneficially Owned
1.Title of Security (Instr. 3)	2. Trans. Date	2A. Deemed Execution Date, if any	3. Trans. Code (Instr. 8)		4. Securities Acquired (A) or Disposed of (D) (Instr. 3, 4 and 5)			5. Amount of Securities Beneficially Owned Following Reported Transaction(s) (Instr. 3 and 4)	6. Ownership Form: Direct (D) or Indirect (I) (Instr. 4)	7. Nature of Indirect Beneficial Ownership (Instr. 4)
			Code	V	Amount	(A) or (D)	Price
Common Stock	4/2/2018		A		1772   (1)	A	$0.00	9826	D

Table II - Derivative Securities Beneficially Owned ( e.g. , puts, calls, warrants, options, convertible securities)
1. Title of Derivate Security (Instr. 3)	2. Conversion or Exercise Price of Derivative Security	3. Trans. Date	3A. Deemed Execution Date, if any	4. Trans. Code (Instr. 8)		5. Number of Derivative Securities Acquired (A) or Disposed of (D) (Instr. 3, 4 and 5)		6. Date Exercisable and Expiration Date		7. Title and Amount of Securities Underlying Derivative Security (Instr. 3 and 4)		8. Price of Derivative Security (Instr. 5)	9. Number of derivative Securities Beneficially Owned Following Reported Transaction(s) (Instr. 4)	10. Ownership Form of Derivative Security: Direct (D) or Indirect (I) (Instr. 4)	11. Nature of Indirect Beneficial Ownership (Instr. 4)
				Code	V	(A)	(D)	Date Exercisable	Expiration Date	Title	Amount or Number of Shares
Stock Option	$149.02							4/27/2014	4/26/2021	Common Stock	3840		3840	D
Stock Option	$204.01							4/25/2015	4/24/2022	Common Stock	2790		2790	D
Stock Option	$245.86							4/24/2016	4/23/2023	Common Stock	2330		2330	D
Stock Option	$248.22							4/30/2017	4/29/2024	Common Stock	2127		2127	D
Stock Option	$231.88							4/1/2018	3/31/2025	Common Stock	3122		3122	D
Stock Option	$234.38							4/1/2019	3/31/2026	Common Stock	3813		3813	D
Stock Option	$231.20							4/3/2020	4/2/2027	Common Stock	2814		2814	D
Stock Option	$276.64	4/2/2018		A		3904		4/2/2021	4/1/2028	Common Stock	3904	$0.00	3904	D

Explanation of Responses:
(1)	Award of restricted stock units to be settled after vesting by the delivery of unrestricted shares of common stock on a one-for-one basis.

Reporting Owners
Reporting Owner Name / Address	Relationships
	Director	10% Owner	Officer	Other
Robbins Paige K 100 GRAINGER PARKWAY LAKE FOREST, IL 60045			Sr. VP, Chief Digital Officer

Signatures
Hugo Dubovoy, Jr., as attorney-in-fact		4/4/2018
** Signature of Reporting Person		Date

Reminder: Report on a separate line for each class of securities beneficially owned directly or indirectly.
*	If the form is filed by more than one reporting person, see Instruction 4(b)(v).
**	Intentional misstatements or omissions of facts constitute Federal Criminal Violations. See 18 U.S.C. 1001 and 15 U.S.C. 78ff(a).
Note:	File three copies of this Form, one of which must be manually signed. If space is insufficient, see Instruction 6 for procedure.
Persons who respond to the collection of information contained in this form are not required to respond unless the form displays a currently valid OMB control number.