Vajda was in the 1982 round of 16 of the junior tournament of the Australian Open . He had his first respectable success in 1985 at the ATP tournament in Kitzbühel , where he defeated Henri Leconte and made it to the semifinals. In 1987 he was in the final in Munich , where he lost to Guillermo Pérez Roldán . In the course of his career he was able to win two individual titles, in 1987 in Prague against Tomáš Šmíd and in 1988 in Geneva against Kent Carlsson . He reached his highest ranking in the tennis world rankings in 1987 with position 34 in singles and in 1990 with position 118 in doubles.
His best individual result at a Grand Slam tournament was reaching the third round of the French Open in 1991. In the doubles competition, he qualified twice for the main field. In Mixed he stood in 1985 alongside Andrea Holíková in the second round of the French Open.
After the end of his professional career, he was temporarily captain of the Davis Cup and Fed Cup teams in Slovakia. From 2006 to the beginning of May 2017 he was the coach of Novak Đoković , since the additional engagement of Boris Becker , Vajda has played a smaller role in the Serbian coaching staff. Since April 2018 he has been coach of Traineroković again.