Anthony George Coe (born 29 November 1934 in Canterbury) is an English composer and jazz musician who plays clarinet, bass clarinet and tenor saxophone.

Coe began his performing career playing with Humphrey Lyttelton's band from 1957 to 1962. In 1965 he was invited to join Count Basie's band ('I'm glad it didn't come off – I would have lasted about a fortnight') and has since played with the John Dankworth Orchestra, The Kenny Clarke-Francy Boland Big Band, Derek Bailey's Company, Stan Tracey, Michael Gibbs, Stan Getz, Dizzy Gillespie and Bob Brookmeyer, and performed under Pierre Boulez as well as leading a series of groups of his own, including Coe Oxley & Co with drummer Tony Oxley. He played clarinet on Paul McCartney's recording of "I'll Give You A Ring", released in 1982, and saxophone on John Martyn's 1973 album Solid Air.