At the end of the 1970s Attila Grószpéter was one of the best Hungarian chess juniors, representing his country in the World Youth Chess Championship in U16, U18 and U20 age groups and European Junior Chess Championship in U20 age group. In 1978, he made his first appearance in the final of individual Hungarian Chess Championship, sharing 3rd place (together with, among others, Iván Faragó). He repeated this result two years later, sharing the 3rd place with László Hazai, and in 1984 he won the bronze medal in the Hungarian Chess Championship. Attila Grószpéter achieved his greatest successes in these competitions in 1993 and 1995, winning silver medals twice.[1]
In 1985, at second reserve board in the 1st World Team Chess Championship in Lucerne (+0, =1, -1) and won team silver medal,
In 1989, at third board in the 2nd World Team Chess Championship in Lucerne (+2, =4, -0) and won individual gold medal.
Attila Grószpéter played for Hungary in the World Youth U26 Team Chess Championship:[6]
In 1981, at first board in the 3rd World Youth U26 Team Chess Championship in Graz (+4, =6, -0) and won team bronze medal.
Attila Grószpéter played for Hungary in the Men's Chess Mitropa Cup:[7]
In 1990, at first board in the 13th Chess Mitropa Cup in Leibnitz (+3, =0, -2) and won team silver medal.
Attila Grószpéter six times played for chess club Zalaegerszegi Csuti-Hydrocomp SK in the European Men's Chess Club Cups (1995-1996, 2001-2004).[8]
In 1979, Attila Grószpéter was awarded the FIDE International Master (IM) title and received the FIDE Grandmaster (WGM) title seven years later. He reached his career highest chess ranking on January 1, 1996 (at that time he had 2565 points), while the highest place on the FIDE world list was the 75th place, which he occupied on July 1, 1990 (with a score of 2555 points).[9] At the same time, he was ranked 5th among Hungarian chess players, after Zoltán Ribli (2610), Gyula Sax (2600), Lajos Portisch (2590) and József Pintér (2565).