Moffett served in the United States Navy, after which he pursued boxing before studying music at Huston-Tillotson College in Austin. Moffett married in 1953 (Coleman was best man, and performed at the wedding),then began teaching music at a public school in Rosenberg, Texas
In 1961, Moffett moved to New York City to work with Coleman, but the saxophonist soon went into a brief retirement period. Moffett worked with Sonny Rollins, appeared on Archie Shepp‘s album Four for Trane, and led a group that included Pharoah Sanders and Carla Bley. When Coleman returned to performing in 1964, he formed a trio with Moffett and bassist David Izenzon.Moffett also performed on vibraphone.