Jacob Nelleman was born in Copenhagen, Denmark. He raced extensively in Denmark winning the Formula 3 Championship twice: in 1976 with a GRD 374 Toyota Novamotor and in 1977 driving a Modus M1 Toyota Novamotor. He made it briefly to Formula One in 1976, with a single entry into the 1976 Swedish Grand Prix. Driving Brabhams run by the RAM team. Despite taking part in qualifying sessions in two cars, a BT42 and a BT44B, he failed to qualify.
His father, Vilhelm Nellemann Jr. was also a racing driver who competed in the 50s and a bit into the 60s. His grandfather, Vilhelm Nellemann Sr., also raced, as did his uncle, Robert Nellemann, who won the Danish F3 Championship 8 times between 1950 and 1965.