Giuseppe Costa is a Palermo double bassist and electric bassist who has been a working jazz musician since 1973. He is listed in the rhythm section of the Sicilian Jazz Orchestra (Orchestra Jazz Siciliana), the big band run by the city's Brass Group, and his biography there calls him one of its founding members. He teaches double bass, electric bass and music theory at the Brass Group's music school and jazz double bass at the "A. Scarlatti" Conservatory in Palermo.

His biography dates his first professional work to 1973 and adds that between 1975 and 1978 he took part in several RAI television broadcasts hosted by guitarist Franco Cerri. His first recording, in 1979, was with the Palermo vibraphonist Enzo Randisi, and Discogs confirms it: Costa plays electric bass on Randisi's four-track LP Enzo Randisi (P.D.R., 1979), a modal jazz-funk record with Randisi's son Riccardo on Rhodes piano and ARP synthesizer. He returned to Randisi's band for the Enzo Randisi Swing Ensemble LP (Ransemble, recorded March 1981), on acoustic and electric bass, and streaming services credit him, with pianist Salvatore Bonafede and drummer Mimmo Cafiero, on Randisi's quartet standards album Ten Years After (Splasc(h), 1991).

Formal study came in the middle of that run. He took a degree in classical double bass in 1985 and a jazz degree several years later; in 1987 he won a scholarship to the Berklee School of Music in Boston, and in 1989 he studied in Denmark with the bassist Niels Pedersen. With the drummer Pippo Cataldo (billed on some credits as Giuseppe Cataldo) he founded the Costa-Cataldo Music Project. Their first record, Picture Number One (Splasc(h) Records, 1988), was recorded at Sud Record Studios in Palermo in August 1987 with Salvatore Bonafede on piano and a horn front line of alto saxophone, two trombones and trumpet; Costa plays acoustic bass and shares the producer credit with Cataldo. The follow-up, Picture Number Two (Splasc(h) Records, 1990), is billed to Cataldo and Costa with a four-horn front line that includes trumpeter Flavio Boltro and trombonist Danilo Terenzi; Discogs lists Costa on bass and as co-producer.

From the 1990s on he is mostly a sideman, and a busy one: his biography counts about 40 recordings. Discogs itemizes several of them. On pianist Giovanni Mazzarino's Thinking Miles (MM Records, 1995) he plays acoustic bass in a band with drummer Ettore Fioravanti; on the Daniele Sala Trio's Introducing Series Vol. 1 (Philology, 2004), recorded in Palermo in 2002 and 2003, he is one of three bass players credited, beside Ares Tavolazzi and drummer Massimo Manzi; and he plays bass on two Dixieland-repertoire albums led by pianist Claudio Lo Cascio, New Orleans Memories (C.R. Records, 2015, with his Sicilia Jazz Dixielanders) and Nick La Rocca - The Last Records (C.R. Records, with the Sicilia Jazz Big Band), the latter also featuring the tenor saxophonist Francesco Marchese. He also plays double bass on two tracks of Cataldo's contemporary-classical LP Sincronie (C.R. Records, 1988).

The Sicilian Jazz Orchestra is the largest part of his public record. The Brass Group describes it as the first and only permanent jazz orchestra in Italy with public participation, founded in the early 1970s by Ignazio Garsia as the Brass Group Big Band, and its current conductor is Domenico Riina. Costa's biography says it has been conducted by Gil Evans, Vince Mendoza, Clark Terry, Mel Lewis, Bob Mintzer and Peter Erskine. The same biography says he has performed with Bob Berg, Patti Austin, Mal Waldron, Tony Scott, Paolo Fresu, Enrico Rava, Stefano Bollani, Martial Solal and John Lewis. Those are his own account of his career; Discogs carries no recording credit for him with any of them.

Costa is a versatile rhythm-section bassist whose documented work runs from 1970s electric jazz-funk to bop-rooted small-group playing, big-band section work and traditional jazz. Discogs tags the 1979 Randisi LP Modal and Jazz-Funk and Picture Number One Contemporary Jazz; Thinking Miles is built around Miles Davis, Monk and Horace Silver repertoire, with "Off Minor", a Horace Silver medley and an "I Remember Monk" medley among its eleven tracks; Ten Years After is a standards date with "When I Fall in Love", "My Foolish Heart" and "Con Alma"; and the Lo Cascio albums play early New Orleans and Dixieland repertoire ("Tiger Rag", "Basin Street Stomp", "Jazz Me Blues"). His schooling combines a classical double-bass degree, a jazz degree, a Berklee scholarship and study with Niels Pedersen, the Danish bassist named in his biography.