In the World Cup, Velichkov debuted in the first round of the 1979–80 World Cup in Ruhpolding in West Germany. Over his career he finished twice on the podium. Both came in Murmansk in the last round of his debut season, a second place in the 20 km individual and a third in the 10 km sprint. These podium finishes were the first for a Bulgarian biathlete, and, as of the end of the 2014–15 season, the last by a male Bulgarian biathlete. He also finished in the top ten in multiple other races. These finishes were not matched by any other male Bulgarian biathlete but his contemporary Spas Slatev until the 2014–15 season, where Krasimir Anev finished 4th in a mass start race in Oberhof, and Vladimir Iliev finished 6th twice during the 2015 World Championships in Kontiolahti. Velichkov was a part of the relay team that finished 6th in the World Cup race in Ruhpolding in 1988, which is still the best relay finish by a male Bulgarian relay team. Velichkov's best overall finish came in the 1981–82 World Cup where he finished 9th, the best overall finish by any male Bulgarian biathlete.