In 1998, Svec achieved his first success in wrestling, when he won the silver medal, against Russia's Gogi Koguashvili at the World Championships in Gävle, Sweden.
After long years of defeat and struggles in the competition, Svec finally managed to repeat his silver medal at the 2006 World Championships in Guangzhou, China, losing out to Estonia's Heiki Nabi by a technical score of 1-3.