Baker played the guitar until his mid-teens, at which point he began to take an interest in the bass as well. He played in The John Etheridge/Ric Sanders Group in the early 1980s. He has also worked with his own group, the Fred Thelonious Baker Group who recorded a self-titled album in 1984. Baker has recorded several albums with Harry Beckett. They have also made a concert tour in Europe together. Baker accompanied Beckett's band on a Charles Mingus tribute tour in the UK. Other artists Baker has worked with include Horace Parlan, Vikki Clayton and Elton Dean.