He was born in New York, New York and began learning the saxophone when he was 15 and by age 16 he began to tour with an band. He returned to New York City and became a session musician. During the Swing Era, his big band was very popular with hits like Begin the Beguine.
Throughout his musical career, Shaw would take sabbaticals where he would quit the business and pursue a writing career.
Shaw was married eight times. Among them were actresses Ava Gardner and Lana Turner. He also married Betty Kern, daughter of songwriter Jerome Kern. Since 1957 he has been married to actress Evelyn Keyes.
In 1955, Shaw stopped playing the clairinet. He has since concentrated on writing, concentrating on semi-biographical fiction.