In 1964 Greene finished seventh in downhill at the Innsbruck Olympic Winter Games. In 1967, Nancy Greene won the first Alpine skiing World Cup. The following year she competed in the 1968 Grenoble Olympic Winter Games, finishing tenth in the downhill and winning silver in the slalom.
The giant slalom in Grenoble was Greene's last chance for a victory. She skied a near-perfect race, but when she turned around to look at the electronic clock, the numbers were still moving. Greene thought, "I've just skied the race of my life and they missed my time”. Then the clock malfunction was corrected and her time appeared – she had won the race by 2.64 seconds, the largest margin in the event's history.
Following her retirement from competition, she has made a major contribution to Canadian sport since accepting an appointment to the government's "Task Force on Sport For Canadians”.