Crespo turned professional in 1951 with the Spanish team P.C.
[3] He finished 39th in the general classification of the 1957 Vuelta a España.
Crespo's last win was the GP de Martorell in 1959.
Crespo retired from cycling at the end of the 1959 season.
[4] His father, Antonio Crespo Sanjuán, was one of the pioneers in the sport in Catalonia.