Velimir competed at the 2009 European Youth Olympic Festival. He won a gold medal in 100m butterfly and silver in 100m Freestyle. At the 2010 Youth Olympic Games, he was a Serbian flagbearer and won 2 medals, silver in 100m Freestley and bronze in 100m butterfly therefore Olympic Committee of Serbia has declared him the best young athlete in 2010. Stjepanović won gold medals in the 100m freestyle and 100m butterfly at the 2011 European Junior Swimming Championships.