Duško Gojković (Serbian Cyrillic: Душко Гојковић; born 14 October 1931) is a Bosnian jazz trumpeter, composer, and arranger.

Gojković was born in Jajce (ex-Yugoslavia, now in Bosnia-Herzegovina). He studied at the Belgrade Music Academy from 1948 to 1953. He played trumpet in dixieland bands and joined the big band of Radio Belgrade when he was eighteen. He moved to West Germany and first recorded as a member of the Frankfurt Allstars in 1956. He spent the next four years as a member of Kurt Edelhagen‘s orchestra.

In these years, Gojković played with Chet Baker, Stan Getz, and Oscar Pettiford. In 1958, he performed at Newport Jazz Festival and drew attention on both sides of the Atlantic Ocean. In 1961, Gojkovic received a scholarship to attend Berklee College of Music, where he studied with Herb Pomeroy