After graduating from Boston Latin School in 1937 and Harvard College in 1941, Levenson enlisted in the United States Navy in 1942. He attended Japanese Language School and saw active service in the Solomon Islands and Philippines campaigns. After the war he earned M.A. (1947) and PhD (1949) degrees at Harvard, where he was a student of John K. Fairbank. He was a member of the Harvard Society of Fellows. He taught at the University of California, Berkeley, from 1951 until his death. He drowned in a canoeing accident in the Russian River, California, in 1969.