As of April 2007, his Elo rating was 2480, making him the # 25 player in Israel and the 887th-highest rated player in the world.
In 1974, Gruenfeld won the Israeli championship for youth players. In 1978, he tied for 2nd-5th in Skien. In 1978, he won in Gausdal. In 1979, he tied for 1st-2nd in Biel. In 1979, he took 2nd in the Lucerne Zonal. In 1979, he took 12th in the Riga Interzonal, won by Mikhail Tal.
In 1980, he tied for 3rd-4th in Beer Sheva, tied for 2nd-8th in Lugano, tied for 2nd-4th in Gausdal, tied for 1st-4th in Oberwart, tied for 2nd-5th in Ramat Hasharon, and won in Biel. In 1981, he tied for 1st-3rd in Lugano, and won in New York.
In 1982, Gruenfeld won the Israeli championship. In 1984, he won in Dortmund. In 1985, he was equal first with Maxim Dlugy and Dmitry Gurevich at the 13th World Open of Philadelphia (Dlugy won the play-off). In 1987, he won the Munich Zonal). In 1987, he tied for 8-11th in the Zagreb Interzonal, won by Viktor Korchnoi. In 1990, he again won the Israeli championship.
- In 1978, at second reserve board in the 23rd Olympiad in Buenos Aires (+2 –0 =7);
- In 1980, at third board in the 24th Olympiad in La Valletta (+6 –3 =2);
- In 1982, at first board in the 25th Olympiad in Lucerne (+2 –2 =7);
- In 1984, at first board in the 26th Olympiad in Thessaloniki (+3 –4 =4);
- In 1990, at second board in the 29th Olympiad in Novi Sad (+0 –3 =5);
- In 1992, at first reserve board in the 30th Olympiad in Manila (+4 –1 =4).