Gunsur was born in 1975 as the second child of a family of Tatar descent (a Turkic ethnic subgroup). His mother, Sibel, was a lecturer and his father, Teoman, was an industrial engineer who graduated from the Middle East Technical University and worked in a nuber of different sectors.

His older sister Zeynep Gunsur Yuceil, who is a choreographer of modern ballet, is also a lecturer. He began his acting career at the age of seven in various commercials. At the age of 14, he appeared in Okan Uysaler's Past Spring Mimoses with actors such as Rutkay Aziz, Filiz Akin and Musfik Kenter.