Griga played in his childhood and youth at MŠK Žilina. For the season 1981/1982 it undertook Sparta Prague. 1986/1987, the striker played for Dukla Prague. Then he returned to Sparta Prague. In 1990, Griga to Feyenoord Rotterdam. He went in 1992 to Rapid Vienna and finished his career there. He participated in the 1990 World Cup in Italy. Griga completed 246 games in the 1st Czechoslovak league and scored 123 goals. In his career he scored 137 goals, including 120 for Sparta Prague, three for Dukla Prague, ten for Feyenoord and ten for Rapid Wien. For Czechoslovakia, he made 34 international matches in which he scored eight goals.
After end of his career as a player Griga worked a half years as a lawyer. For the 1995/1996 season, he took over as coach at second division MŠK Žilina, with which he ascended into the first league. He switched to FK AS Trenčín and repeated his previous success. In 1998 he became coach of Slovan Bratislava, with whom he got the double. He then took over the Slovak U20 selection and after half a year the U21 national team. In December 2001 he went to FK ZTS Dubnica, he left for health reasons in the fall of 2003. In December 2003, he accepted an offer from Slovan Liberec, in June 2005, he resigned. In October 2005, it undertook Sparta Prague as their new coach. On 2 September 2006, he was released after a moderate start to the season as coach of Sparta Prague. For the season 2007/ 08 he took over the Prague FK Viktoria Zizkov Erstligaaufsteiger. After an unsuccessful start to the season Griga was released in early September 2008. Since May 2011, he was coach of the Slovakian first division side FK Senica. On April 26, 2012, he resigned as coach of the Slovak national team in his office, but was dismissed in June 2013 after more than a year of work.