Born in Bors, Johan Rasmussen has competed in three World Championships and the 1994 Olympics and made his World Ski Championships debut in March 1990 with a 21st place in rnskldsvik, and made three starts in 1991.
He made his World Cup debut in March 1990 with a 71st place in Ornskoldsvik, and made three starts in 1991. He also participated in the 1991 World Ski Championships. 
