Using first principle electronic structure calculations within density functional theory and the supercell model, we have investigated the nature and formation energies of defect states associated with Ga and Te vacancies and Ge and Sn substitutional impurities in GaTe. We have also calculated the band structure of pure GaTe for comparison with systems with defects and also to find out the importance of spin-orbit interaction (SOI) on its band structure. We find that the top valence band at the Γ-point shifts up in energy by ∼0.1 eV due to the mixing of Te p(x)-p(y) and p(z) bands, this splitting being considerably smaller than in atoms where it is ∼0.8 eV. From an analysis of charge densities and band structures associated with the defect states, we find that most of them are strongly localized and lie deep in the band gap region. The calculated binding energy of the deep defect state and the ε(-1/-2) transition level associated with the Ga vacancy appears to be in good agreement with experiment. Formation energy calculations suggest that V(Ga) is the preferred intrinsic defect in GaTe.