Giuseppe Costa starts his concertistic activity in 1973. He participates between 1975 and ’78 to some Rai television broadcasts conducted by Franco Cerri: “Sapere, Jazz in Italia”, “Chitarra e fagotto” and “Di Jazz in Jazz”.
In 1979 he records with the group of the vibraphonist Enzo Randisi, with whom he does various tours. From ’73 to ’80 he is a chorist of “Cantori Nuovi” group of Norino Buogo, having concerts in the main sicilian theaters. For a short period he is the first contrebass of the orchestra of the Ente Autonomo Teatro Massimo of Palermo directed by John Lewis. In 1984 he records a disk with the Reinhardt Jazz Studio Orchestra directed by Enrico Intra.
In 1986 he performs as a solist with the Orchestra Sinfonica Siciliana directed by Ignazio Garsia with the partecipation of the harmonica player Toots Thielemans. In 1986 he graduates in contrabass at the conservatory “A.Scontrino” of Trapani under the guidance of Maestro F. Muzzi, in 1987 he wins a scholarship at the Berklee School of Music of Boston and in 1989 he perfectionates in Danemark with the contrabassist Niels Pedersen. He forms with the drummer Pippo Cataldo the group Costa-Cataldo Music Project with which he records “Pictures n° one” in 1987 and “Pictures n° two” in 1990.
In 1996 he forms a duo with the pianist Marvi La Spina. He collaborates on a continuous basis with the Orchestra Jazz Siciliana, the Orchestra da Camera Kandinskij and Duke Ellington Singers. He formed a trio with Rita Collura on the soprano sax and Marvi La Spina on the piano.