A former midfielder, his career achievements saw him inducted into the Viktor Leonenko Hall of Fame in March 2012.

Born in Kherson, Ukrainian SSR, Soviet Union, Maksymov played for Valery Lobanovsky's Dynamo Kyiv in his native Ukraine.

In November 1997 he moved to Germany joining Bundesliga club Werder Bremen, signing a contract until 2001.

Bundesliga side Waldhof Mannheim on a free transfer in 2001, along with Bernhard Trares.

[citation needed] Maksymov earned 27 caps playing for the Ukraine national team scoring give goals.