Parra's most successful season was from 2001 to 2002. At the 2002 Winter Olympics, he took the gold in the 1500 meters, an event in which he had been expected to do well but faced a deep pool of competition. Before that, he won the silver in the 5000 meters being bested by Jochem Uytdehaage of the Netherlands. He has worked part-time in Home Depot's gardening department in West Valley, Utah. In his book, Reflections in the Ice, Parra recounts pursuing his dream of becoming an inline skater at 17, working at McDonald's in Tampa, Florida, and being so poor he had to eat out of the trash.
Parra was selected to take over as U.S. speed skating national all-around coach for the 2010 Olympics.