She won her first Yugoslav Chess Championship national title in 1983 jointly with her fellow counterpart Marija Petrović.

Maksimović had her first major success in 1980 when she won the title of European Junior Chess vice champion in the U20 age group.

Suzana Maksimović won the Yugoslav Women's Chess Championships two times: 1983 and 1991 - together with Mirjana Marić.

In 1990 in Pula, Suzana Maksimović shared the 1st-4th in the Women's World Chess Championship Zonal Tournament.

She participated four times in the Women's World Chess Championship Interzonal Tournaments: Maksimović played for Yugoslavia and Serbia in the Women's Chess Olympiads:[5] She received the FIDE title of Woman International Master (WIM) in 1982 and Woman Grandmaster (WGM) in 1999.