Maksimović got his BA (1961), MA (1965) and PhD (1971) in history at the Faculty of Philosophy of Belgrade University.
From 1996 he is the vice president of the Association Internationale des Etudes Byzantines.
In 1998 he became also director of the Institute for Byzantine Studies of the Serbian Academy of Sciences and Arts.
[citation needed] He worked as a visiting professor in École des Hautes Études en Sciences Sociales (Paris), Max-Planck Institute für europäische Rechtsgeschichte (Frankfurt/Main), Cologne University and University of Crete.
[citation needed] Maksimović won a number awards for his achievements including the City of Belgrade Award (1973), Scientific Medal of Sofia University (1989), Vladimir Ćorović prize for the achievements in historiography (2011).