Grgur was the eldest son of Serbian Despot Đurađ Branković and Eirene Kantakouzene.

In 1458, during the struggle for the throne of the Serbian Despotate, Grgur resurfaced claiming it for himself or his son.

Đurađ had intention to mobilize forces to recover his lost territories of Serbian Despotate.

On 8 May 1441 both Grgur and his brother Stefan were blinded, based on the order of Sultan Murad II.

[4][5] According to John Van Antwerp Fine, Jr. and Sima Ćirković, Grgur resurfaced in 1458, claiming the succession of the vacant throne of Serbian Despotate for himself or his son.