The energetics of native point defects in GaSb is studied using the density-functional theory within the hybrid functional scheme (HSE06). Our results indicate that the Ga Sb antisite has the lowest formation energy and could thus be the acceptor defect responsible for the p-type conductivity of undoped GaSb. We find also that the Sb Ga antisite has a remarkably low formation energy in Sb-rich growth conditions and it should act as a donor for all Fermi level positions in the band gap. However, we suggest that the structural metastability of the Sb Ga antisite or extrinsic point defects, namely carbon and in particular oxygen, may neutralize its compensating character.