Jimmy Cozier Sr. (born 1954) is a jazz musician from New York City. He plays saxophone, flute, and clarinet. He is the father of R&B singer Jimmy Cozier. He has performed and toured with Panama Francis, Sam Rivers, Reggie Workman, Mongo Santamaria, and Abdullah Ibrahim. He played lead alto saxophone with the big bands of Cab Calloway, Frank Foster, Charlie Persip, Jaki Byard, and Chico O'Farrill.