Gustave "Gus" "Gussie" Mueller (New Orleans, Louisiana April 17, 1890 - Hollywood, California December 16 1965) was an early jazz clarinetist.

Mueller was one of the top clarinetists with Papa Jack Laine's bands in New Orleans before going to Chicago with Tom Brown's band in early 1915. After serving in the Army in World War I he moved to California and joined the early Paul Whiteman Orchestra, with which he moved to New York City. He helped give Whiteman an idea of the New Orleans jazz style. One of the Whiteman Orchestra's early hit records, as well as one of the unfortunately few recordings where Mueller can be heard prominently, is The Wang Wang Blues which Mueller dominates in a style similar to Larry Sheilds while somewhat foreshadowing the early work of Sidney Bechet. While Mueller shares composter credit on "Wang Wang", some of his New Orleans contemporaries said the number was all his and he had featured it before joining Whiteman. As Paul Whiteman started taking himself more seriously and began demanding arrangements with little room for improvisation, Mueller left the band in disgust in 1924, saying "You call yourselves a jazz band, but you can't play the blues worth a damn".

Mueller returned to California to join his old friend (and fellow Tom Brown Band alumnus) Ray Lopez in the Abe Lyman Orchestra. Mueller stayed in the Los Angeles area, playing with dance bands, novelty and "Hillbilly" bands, and working on motion picture soundtracks before retiring after World War II.