He graduated from the University of Belgrade Faculty of Philosophy. He is an editor for the Vijesti newspaper for its culture section and is deeply involved with the preservation of the original Montenegrin language. He is a member of the Montenegrin PEN Center. He was also a speaker at the International Festival for short stories in 2009.
Brković published collections of poetry: Konji jedu breskve (1985), Filip boje srebra (1991), Rt Svete Marije (1993), Contrapposto (1998) and Dvojenje (2001) and novels Privatna galerija (2002) and Paranoja u Podgorici (2010).