Joe Puma (August 13, 1927 – May 31, 2000) was an American jazz guitarist.

Puma was born in the Bronx, New York. His first professional experience came with Joe Roland in 1949–50. He played in the band led by Cy Coleman. He acted as a session musician for many jazz musicians of the 1950s, including Louie Bellson, Artie Shaw's Gramercy Five, Eddie Bert, Herbie Mann, Mat Mathews, Chris Connor, and Paul Quinichette, Lee Konitz, and Dick Hyman; he also recorded extensively as a leader at this time. In the 1960s he worked with Morgana King, Bobby Hackett, Gary Burton, and Carmen McRae, and between 1972 and 1977 he and Chuck Wayne led an ensemble. He continued to perform and teach into the late 1990s.

In 1957 he won the New Star Award for Guitar from Metronome Magazine.
East Coast Jazz Series (Bethlehem, 1954)Joe Puma Quintet (Bethlehem, 1954)Wild Kitten (Dawn, 1957) with Steve Lacy, Herbie Mann, Oscar PettifordJoe Puma Jazz Trio and Quartet (Jubilee, 1957)Like Tweet (Columbia, 1961)Interactions (Candid Productions/City Hall, 1974)Shining Hour (Reservoir, 1984) with Hod O'Brien and Red MitchellIt's a Blue World (Euphoria Jazz, 1999) with Murray Wall and Eddie LockeWhat Is There to Say? (Nagel Heyer, 2000) with Warren VachéThe Jazz Guitar of Joe Puma (Fresh Sound, 2007) (compilation)With Herbie Mann
Herbie Mann Plays (Bethlehem, 1956)Flamingo (Bethlehem, 1955)The Herbie Mann-Sam Most Quintet (Bethlehem, 1955)Love and the Weather (Bethlehem, 1956)Flute Flight (Prestige, 1957) with Bobby JasparFlute Soufflé (Prestige, 1957) with Bobby JasparSultry Serenade (Riverside, 1957)Salute to the Flute (Epic, 1957)The Jazz We Heard Last Summer (Savoy, 1957)Yardbird Suite (Savoy, 1957)With Chris Connor
1955 This Is Chris1957 Chris1957 Chris Connor Sings the George Gershwin Almanac of Songs1998 All About RonnieWith Mark Murphy
1975 Mark Murphy Sings1992 Stolen...And Other Moments1998 Jazz Standards1999 SongbookWith Morgana King
1992 This Is Always1997 Every Once in a While1998 Looking Through the Eyes of Love2000 Tender MomentsWith others
1955 Encore, Eddie Bert1955 Joltin' Joe Roland, Joe Roland1954 Skin Deep (Norgran)1956 Bernie's Tunes, Bernard Peiffer1956 Special Delivery, Janet Brace1956 The Four Most, Jimmy Raney1956 The Modern Art of Jazz by Mat Mathews, Mat Mathews1957 For Lady, Webster Young (Prestige)1963 The Groovy Sound of Music, Gary Burton1965 Alive!, Carmen McRae1973 Interactions, Chuck Wayne1979 Chasin' the Bird, Helen Merrill (EmArcy)1992 Last Recordings: Rare and Unreleased, Artie Shaw1993 Horn of Plenty, Warren Vache1998 My Shining Hour, Gail Wynters (Naxos)1999 Trav'lin' Light/Merely Marvelous, Jimmy Giuffre2000 Blues of Summer, Wycliffe Gordon2000 Have Tenor Sax Will Blow/Live at Small's Paradise, King Curtis2001 Jaywalkin' , J. R. Monterose2003 Soul Eyes: The Mal Waldron Memorial Album, Mal Waldron2004 The Complete Whitey Mitchell Sessions, Steve Lacy