The top Hungarian distance swimmer of his age, Katona earned his first success at the 1958 Europeans, winning a silver in the 1,500 m freestyle and a bronze in the 4 x 200 m relay. Four years later, he upgraded to gold in the 1,500 m, his greatest international success. At the Olympics, he managed to reach the final of his best event, the 1,500 m, twice, placing 5th (1960) and 8th (1964). He also won 13 Hungarian titles in the freestyle events. In addition to his swimming exploits, Katona was also a national level water polo player, being selected for the national team 17 times. With Egri VK, he won the national cup in 1972, beating Ferencváros in the final. Katona later became a physical education teacher, and also remained involved with the Egri swimming club, eventually becoming its president.