Kiss made his international debut for the Four Hills Tournament in 1961/62 . After finishing 46th in the opening competition on the Schattenbergschanze in Oberstdorf , he could not prevail in the other competitions either. After 69th place in Innsbruck, 48th place in Garmisch-Partenkirchen and 69th place on the Paul-Ausserleitner-Schanze in Bischofshofen , he was only 48th overall. At the Nordic World Ski Championships in Zakopane , which took place shortly afterwards, in 1962 , he competed in both individual competitions and became 52nd on the normal hill and 57th on the large hill. At the Hungarian Championships in 1962 he won the individual title together with László Gellér .
At the Four Hills Tournament 1962/63 he was able to increase his performance significantly. With 28th place on the Great Olympic Hill in Garmisch-Partenkirchen , he jumped to the best individual placement of his career. In the overall ranking he reached 34th place with 655.3 points after the tour was over. After his performance in the following Four Hills Tournament in 1963/64 collapsed again and he only reached rank 58 in the overall ranking, he jumped again at the Four Hills Tournament 1964/65 in Oberstdorf on rank 32 and was thus his best with rank 30 in the overall ranking Achieve overall result.
At the Nordic World Ski Championships in Oslo in 1966 , Kiss started again in both individual competitions. He finished 53rd on the normal hill and 49th on the large hill.