Using the local spin-density approximation (LSDA) and the (non self-consistent) GW approach, the (quasi-particle) band structure is calculated for MnTe in zinc-blende geometry. Different parameters characterizing the electronic structure are computed for an antiferromagnetic and the ferromagnetic phase and compared with the experiment. The strong Hubbard-type repulsion on the Mn-3d orbitals and the p-d hybridization are seen to be responsible for substantial defects found in the LSDA picture. It is discussed to which extent these can be improved upon by means of the GW approach.