Henry Jacob Levy was born on September 27, 1927, in Baltimore and grew up in the city's northwest side. He took up the saxophone in grammar school, led his first band at Baltimore City College, and spent about three years in the U.S. Navy in the late 1940s, attending the Navy School of Music at a time when service bands and Baltimore dance halls kept players and ideas circulating. He studied at several colleges without finishing a degree, among them William and Mary, an unhappy year at the Peabody Conservatory, and Catholic University in Washington, where he studied composition with George Thaddeus Jones. His interest in odd meters came from concert composers such as Paul Hindemith, Maurice Ravel, and Igor Stravinsky, and it predated Dave Brubeck's Time Out (1959).

In 1953 Levy went to Los Angeles to play baritone saxophone in Stan Kenton's orchestra. He stayed about six months before heading home to be near Gloria Hildebrand, whom he later married, and he later said the stint was worth three years of college. Discogs lists him, uncredited, on baritone saxophone on "All About Ronnie," the flip side of Kenton's Capitol single "Baia." While he was in the band he wrote charts in unusual time signatures that Kenton began trying out in rehearsal, and the two stayed friends until Kenton's death in 1979. Back in Baltimore he joined his family's Independent Beef Co., a gourmet food and wine shop on North Howard Street, where he became the store's wine importer and filled ledger books with score paper. He arranged for Sal Salvador's orchestra on The Beat for This Generation (Decca, 1960), had a tune recorded by June Christy on Off Beat (1961), and in the mid-1960s led a band that played Baltimore-area rooms such as the Mardi Gras Supper Club and the Eastwind catering hall.

His writing reached a wide audience through the West Coast trumpeter and bandleader Don Ellis, whose orchestra was also pushing into unusual meters. Levy's "Passacaglia and Fugue" was one of the pieces that helped Ellis's band make its mark at the 1966 Monterey Jazz Festival and appears on 'Live' at Monterey!. Ellis went on to record Levy's "Alone" on Electric Bath (1968), "Rock Odyssey" and "Antea" on Don Ellis at Fillmore (1970), "Samba Bajada" on Tears of Joy (1971), "Chain Reaction" on Connection (1972), and, on Soaring (1973), "Whiplash," a chart built on 7/4 and 14/8 figures.

Around 1968, after his father's death, Levy sold the family business and persuaded Towson State College to start a jazz program with himself as director, a post he held for about two decades. His Towson State Jazz Ensemble won the outstanding band honors at the 1970 Notre Dame Collegiate Jazz Festival, where his lead trumpeter Tony Neenan was named best lead trumpet, and it won so many contests at the Quinnipiac festival in New Haven that it was eventually asked to stop competing. The college gave him little money for new music, so he wrote most of the band's book himself. The ensemble began issuing its own albums in 1972 and kept it up through the early 1990s, and in 1975 it recorded 2 + 2 = 5, six Levy pieces for the Music Minus One play-along series. His Opus for Overextended Jazz Ensemble was premiered by the Baltimore Symphony Orchestra in 1971.

From 1971 Kenton's own Creative World label documented Levy's charts on one album after another: "Chiapas" on Live at Redlands University, "A Step Beyond" and "Hank's Opener" on Live at Brigham Young University, four pieces on Live at Butler University (1972), then Birthday in Britain, 7.5 on the Richter Scale, Fire, Fury and Fun, Kenton '76, and Journey to Capricorn, which carries his "Pegasus," "90 Degrees Celsius," and title piece. On the Butler album Kenton introduces him as the man largely responsible for the time revolution in modern jazz. Kenton's wife Audrey recalled that band members would groan when he turned up with new music but mastered it.

In his last years Levy turned to arrangements of bebop pieces by Charlie Parker, Dizzy Gillespie, and Tadd Dameron, alongside standards. The Hank Levy Legacy Band, formed in 1992 after he retired from full-time teaching, still plays his music. In 1997 the U.S. Army Field Band's Jazz Ambassadors recorded The Legacy of Hank Levy, and a video documentary, A Head of Time: Ahead of Time, was completed around 2000. His wife Gloria passed away in 1996, and he himself passed away on September 18, 2001, at the Oak Crest Village retirement community in Parkville, Maryland, of congestive heart failure, at the age of 73. The 2014 film Whiplash, directed by Damien Chazelle, takes its title from his 1973 chart and uses pieces of it, and in April 2017 Towson University honored him posthumously at a ceremony with the Legacy Band playing.

Levy wrote big band charts in meters of 5, 7, 9, 11, and 13 beats and their combinations, but he insisted the music should groove rather than read as a puzzle: his stated aim was to give jazz a kick, and listeners often realize only later that the time signature is unusual. He also wrote strong counterpoint, as "Passacaglia and Fugue" shows, and his harmonic voicings were unconventional for the big band idiom of his day. Among his models he named Hindemith, Ravel, and Stravinsky. As an arranger he was fond of stage songs that bebop had adopted, including those of Cole Porter, George Gershwin, and Jerome Kern. The Kenton and Ellis orchestras made him known to professional players, but his larger audience has been school and college bands, which have played his charts for decades because they are difficult yet rewarding, and drum corps and marching bands have used them as well. AllMusic's Scott Yanow called him a strong, if unsung, influence on later arrangers.