Vesković coached the Željezničar Sarajevo[2] and Elemes Šibenik in the Yugoslav Women's League.

[4] Vesković coached men's teams such as Saint Petersburg Lions for the 2000–01 Euroleague season[5] and Arkadia Traiskirchen in the Austrian Bundesliga.

Vesković was appointed four times as the head coach for women's national team of Yugoslavia and Serbia.

He coached SFR Yugoslavia national team at the 1991 European Women Basketball Championship where he won silver medal.

Vesković married Gordana Grubin (born 1972), a Serbian retired basketball player.