Parra qualified for the Spanish squad in the men's team pursuit at the 2008 Summer Olympics in Beijing based on the nation's selection process from the UCI Track World Rankings. He delivered the Spanish foursome of Sergi Escobar, Asier Maeztu, and David Muntaner a seventh-place time of 4:07.883 in the prelims before his team was later relegated and overlapped to New Zealand in the third match round.