After shakedown training along the New England coast, Glennon guarded troops and supply convoys for the occupation of Sicily (9–15 July 1943). It was here that the giant assault on Europe began sweeping in from the sea. She returned to New York on 3 December 1943, then made two round-trip convoy escort voyages to the British Isles and one to Gibraltar. She arrived in New York from Gibraltar on 22 April 1944 and stood out of that port 5 May with a task group which arrived Belfast, Ireland, on the 14th. Assigned to Assault Force “U” of the Western Naval Task Force, she arrived in the Baie de la Seine, France, on 6 June. After patrolling around the bombardment group for submarines and fast German torpedo boats, she joined in gunfire support of troops ashore.

On 7 June she hurled in 430 5-inch shells ashore in support of troops advancing north toward Quinéville. Under command of Comdr. Clifford A. Johnson, she was again approaching her gunfire support station at 0830, 8 June, when her stern struck a mine. A whaleboat picked up survivors while minesweepers Staff and Threat arrived on the scene, one passing a towline while the other swept ahead of the damaged destroyer. Destroyer escort Rich closed in the wake of the minesweepers to assist, then felt a heavy explosion as she slowly rounded Glennon’s stern to clear the area. Minutes later a second explosion blew off a 50-foot section of Rich’s stern, followed by a third mine explosion under her forecastle. She went under within 15 minutes of the first explosion.

Minesweeper Staff found she could not budge Glennon, whose fantail seemed to be firmly anchored to the bottom by her starboard propeller. Most of her crew boarded Staff and those remaining on Glennon lightened her stern by pumping fuel forward and jettisoning depth charges and topside gear. On 9 June salvage equipment was assembled and some 60 officers and men of the Glennon came back on board. The following morning, just as Comdr. Johnson was preparing to resume efforts to save his ship, a German battery near Quinéville found her range. A second salvo hit Glennon amidships and cut off all power. After a third hit, Commander Johnson ordered abandon ship and the men were taken off in a landing craft. Glennon floated until 2145, 10 June 1944; then rolled over and sank. She suffered 25 lost and 38 wounded.

Glennon earned two service stars during World War II.