Norberg participated in the first Olympic competition for female cross-country skiers in 1952 in Norway, where it was a fourth place.
In 1954, she wrote history again after winning Sweden's first World Cup medal ever on the women's side.
She was part of the relay team with Anna-Lisa Eriksson and Sonja Edström-Ruthström who secured a bronze.
At home, she competed for Sidensjö and Vårby IK, and took six Swedish Championship gold medals in ten kilometers and four Swedish Championship gold medals in relay.