Born in 1823 in England, Woon immigrated to the United States and was living in New York when he joined the U.S. Navy. He served during the Civil War as a boatswain's mate and gun captain on the . At the Battle of Grand Gulf, Mississippi, on April 29, 1863, he "had been confined to his hammock several days from sickness, yet insisted on and took command of the gun of which he was captain; fought it for over two hours, and only left it when no longer able to stand". For this action, he was awarded the Medal of Honor a few months later on July 10, 1863.