Grbić was born in Klek in Socialist Republic of Serbia, Yugoslavia. He is Nikola Grbić's brother. He is a member of the Volleyball Hall of Fame. With the national volleyball team of Yugoslavia, he won a gold medal in the 2000 Summer Olympics and a bronze medal in 1996 at Atlanta. His international victories include a silver medal in the 1998 World Championship and a gold medal in the 2001 European Championship.