Moravec represented the Czech Republic at the 2006, 2010, 2014 and 2018. At the 2014 Winter Olympics, he won silver medals in both the pursuit and the mixed relay (together with Jaroslav Soukup, Veronika Vítková and Gabriela Soukalová) and a bronze medal in the mass start. His best World Cup overall finish yet was 6th in the 2014–15 season.