Claudia Giordani is the daughter of TV sports journalist Aldo Giordani. She began skiing at the age of 10, with Ski Club Sestriere and won the Italian Junior Championships at age 15, dÃ©buting at the World Cup the same year. Two years later she stood on a World Cup podium for the first time in a giant slalom race in Japan and won gold and bronze at the European Junior Championships. Her first World Cup victory came in the following year, again in a giant slalom, this time in France, and she won another two more World Cup races in 1977 and 1980. The highlight of her career was the silver medal in the slalom at the 1976 Olympic Winter Games. She won 17 medals at Italian Championships including 14 titles (6 giant slalom, 5 slalom, 2 combined, 1 downhill) before retiring at the end of the 1980-81 season, only 25 years old. In her last year competing she won gold (slalom) and silver (giant slalom) at the 1981 Winter Universiade.
In 1977 Giordani was appointed Knight of the Order of Merit of the Italian Republic. After retiring from racing, she started a marketing and communication business and became a television commentator for alpine skiing. In 2010 she became president of the regional committee of FISI, the Italian winter sports federation.