Bećković was born in Senta,[1] in the multiethnic province of Vojvodina (then Danube Banate, Kingdom of Yugoslavia), to a military family of Montenegrin Serbs.

Bećković's father Vuk was an officer in the Royal Yugoslav Army, and during World War II the commander of the Rovci Chetnik Battalion and as such, one of the commanders of the leader of the Montenegrin Chetniks, Pavle Đurišić.

Bećković is a close friend of Serbian former Prime Minister Vojislav Koštunica, and an active supporter of his Democratic Party of Serbia.

However, as a prominent Serb nationalist he fiercely advocated against Montenegrin independence, actively supporting the State Union during the pre-referendum campaign.

In April 2022, Bećković signed a petition calling for Serbia not to impose sanctions on Russia after it invaded Ukraine.