Her father Dave Murray was a ski racer and belonged to the " Crazy Canucks " in the 1970s ; he died when she was two years old. Her mother Stephanie Sloan was also a freestyle skier and won the overall ranking of the World Cup in 1979 .
Julia Murray was accepted into the newly created Canadian national ski cross team in 2007. On January 12, 2008, she took part in a World Cup race for the first time in Les Contamines and finished in eighth place. As a result, she was able to establish herself at the top of the world and achieved several placements among the top ten. She achieved her first podium placement on March 14, 2009 as third in Hasliberg . Her best result so far is a second place, achieved on January 9, 2010 in Les Contamines.
At the 2010 Winter Olympics , Murray was eliminated in the quarter-finals and classified as twelfth, whereupon she ended the season early. In the 2010/11 season Murray did not get past eleventh place in the World Cup, but still qualified for the 2011 World Cup in Deer Valley and won the silver medal.