USS Woodrow R. Thompson (DD-721) was a planned United States Navy Gearing-class destroyer laid down during World War II but never completed. Woodrow R. Thompson was laid down on 1 August 1945 by the Federal Shipbuilding and Drydock Company at Newark, New Jersey. The end of World War II in August 1945 resulted in the termination of the contract for her construction on 12 December 1945. The award of the contract was reinstated in early 1946, and she was launched as planned on 16 March 1946, sponsored by Mrs. Robert L. Thompson, the mother of Sergeant Woodrow R. Thompson, a posthumous United States Marine Corps recipient of the Navy Cross.