Katona was born in Eger, Heves, Hungary. As a 17-year-old, Katona represented his country at the 1958 European Aquatics Championships which were held in Budapest, Hungary. In the 1500 metres he came second behind Ian Black to win the silver medal, and also won a team bronze medal in the 4 x 200 metres freestyle relay. Four years later in Leipzig at the 1962 European Aquatics Championships, Katona returned home with a gold medal in the 1500 metres freestyle. At the 1960 Summer Olympics in Rome, Katona reached the final of the 1500 metre freestyle where he finished in 5th place, but in the 400 metre freestyle and 4 × 200 metre freestyle relay he failed to qualify from the first round heats. Four years later at the 1964 Summer Olympics it was the same pattern, he failed to reach the finals in the 400 metre freestyle or the 4 × 200 metre freestyle relay, but in the 1500 metre freestyle he managed to finish eighth in the final.