[1] He won the World Championship for boys Under-16 in Spain in 1996, and was awarded the International Master title.

In the European Junior Chess Championship of 1998, held in Mureck, he scored 6.5/9 for a shared second place.

[2] In 2003, Moiseenko scored 8.5/13 at the European Individual Chess Championship in Istanbul for a shared 4-11th place.

In the same year he won the Toronto Chess'n Math Association Futurity with 8.5/10 and the Canadian Open Chess Championship in Kapuskasing with 8/10.

In 2007, Moiseenko won the Arctic Chess Challenge in Tromsø scoring 7.5/9, half point ahead of Kjetil A.

[4] Moiseenko tied for first, with 6.5/9, in the 2008 Canadian Open Championship in Montreal,[5] and he also won the 2008 Edmonton International tournament, with 7/9, ahead of former U.S. champion Alexander Shabalov.

[7] He won a silver medal in chess at the 2017 Maccabiah Games in Israel, behind German Georg Meier.