The spin polarized first principles pseudofunction (PSF) method with the local spin density approximation (LSDA) has been used to calculate total energies, electronic structures and total and partial densities of states for bulk MnTe in the NiAs structure for both anti-ferromagnetic and ferromagnetic states under the pressure. For the pressure range considered in this study, the anti-ferromagnetic state is thermodynamically more stable than the ferromagnetic state in agreement with experimental observation. For the anti-ferromagnetic state, MnTe has an indirect band gap, which decreases linearly with the increase of the pressure in agreement with experiment. The calculated valence band and conduction band are found to broaden with the increase of the pressure, which can be attributed to the pressure induced shortening of the Mn-Te bond length that enhances hybridization between Mn and Te orbitals.