He reached his peak strength in the early to mid-1970s and in 1973, was awarded the title of International Grandmaster by FIDE, the governing body.
In other competition, he achieved outright or shared first place at Hastings 1973/74 (with László Szabó, Tal and Jan Timman), Baku 1977, Tallinn 1979, Kladovo 1980, Dortmund 1981 (with Jon Speelman and Ľubomír Ftáčnik) and Bangalore 1981.
Other notable results included Lvov 1978 (third equal after Yuri Balashov and Rafael Vaganian) and Tallinn 1985 (second after Sergey Dolmatov).
Gennady Kuzmin was a chess trainer in Ukraine and along with Yuri Kruppa, had helped rising star Kateryna Lahno become the world's youngest Woman Grandmaster.
He was also a trainer to Ruslan Ponomariov when he became the youngest (FIDE) world champion in history, at 18 years and 104 days.