Born James Mundy in Cincinnati, Ohio, he began developing his arranging skills in the 1920s while playing with local bands led by Erskine Tate, Tommy Miles, and Carroll Dickerson. In 1932 he wrote and sold a few arrangements to Claude Hopkins, and at about the same time joined Earl Hines' famous "Grand Terrace" ballroom band in Chicago. Hines hired him originally as a saxophonist, for whom he worked over the course of the next four years. During this period Mundy developed a reputation as a prolific arranger in the emerging "swing" style and began writing and selling arrangements to other bandleaders in order to supplement his income.
Late in 1935 following the triumphant success Benny Goodman and His Orchestra enjoyed in Los Angeles at the Palomar Ballroom, Goodman and his band worked their way east to Chicago where they began their historic six-month booking in the Joseph Urban room of the Congress Hotel. After selling one of his arrangements to Goodman, Goodman hired Mundy on a full-time basis. From then until 1938, Mundy became one of Goodman's principal staff arrangers, joining Spud Murphy and Fletcher Henderson who were already in Goodman's employ. While the Goodman band's book of dance arrangements had heretofore been primarily written by Murphy with its distinctive swinging jazz arrangements contributed by Henderson, from the moment he was hired, it was Mundy who Goodman relied upon to create many of the band's up-tempo "flag-waving" musical numbers, that in time became some of Goodman's most popular numbers. Mundy's list of "killer-dillers" (as they became known as in the popular music journals of the period) include the 1936 (revised) version of "Bugle Call Rag", "Jam Session" (an original composition by Mundy), and the band's 1937 adaptation of Cole Porter's "Ridin' High". His seminal 1937 arrangement of "Sing, Sing, Sing", in many respects defined the Goodman band's position in jazz as well as the band's dominance of the entire music industry, as the "Swing Era" was on the rise in the United States as a cultural phenomenon and popular music style. Mundy was also equally adept at arranging standard popular tunes for the band as well: "You Turned The Tables On Me" (1936) and "And the Angels Sing" (1939), two of the Goodman band's biggest vocal hits, sung by Helen Ward and Martha Tilton respectively, also were both arranged by Mundy.
When Goodman's drummer Gene Krupa left the band in 1938, Mundy left it shortly after as well in order to write for Krupa's new outfit, although he continued to contribute scores to Goodman on a free-lance basis. He briefly led his own band in 1939 and throughout the 1940s Mundy supplied a significant number of original compositions and arrangements to Count Basie (ca. 1940 to ca. 1947), Artie Shaw (1944–45), Dizzy Gillespie (1949), Harry James, Charlie Spivak, Paul Whiteman and many others. He wrote the score to the 1955 Broadway musical The Vamp which starred Carol Channing. The 1957 musical Livin' The Life and the 2010 dance revue Come Fly Away also used some of his music.
- 1937–1947: Jimmy Mundy 1947–1947 (Classics)
- 1958: On a Mundy Flight (Epic)
- 2002: Fiesta in Brass (Golden Era)
With Illinois Jacquet
- The Soul Explosion (Prestige, 1969)
With Sonny Stitt
- Sonny Stitt & the Top Brass (Atlantic, 1962)
- Jimmy Mundy at the Internet Broadway Database
- Ian Carr, Digby Fairweather, & Brian Priestley. Jazz: The Rough Guide. ISBN 1-85828-528-3
- Richard Cook & Brian Morton. The Penguin Guide to Jazz on CD 6th edition. ISBN 0-14-051521-6
- Scott Yanow, Swing Miller Freeman Books, 2000
- Jimmy Mundy — brief biography by Scott Yanow, for AllMusic