Leius was the boys' singles champion at the 1959 Wimbledon Championships. He won the Soviet Championships in 1963, 1964, 1965 and 1968. Other good performances during his career include reaching the final of the 1964 Queen's Club Championships, which he lost to Roy Emerson, and taking Rod Laver to five sets at the 1969 Heineken Open. He was a gold medalist in the mixed doubles at the 1970 Summer Universiade in Turin, with Tiiu Parmas.