Nordström was third at the Nordic Championships in Denmark in 1959. In 1962 he took part in the first European championships in orienteering and took third place behind the Norwegian Magne Lystad and Bertil Norman from Sweden on the 16.5 km distance as the crow flies with 13 posts. With the team from Tierps IF he won the Tiomila in 1966 .
Together with Peo Bengtsson, he is considered to be one of the pioneers of the O-ring , which has been held annually in Sweden since 1965.
