The electronic structure and magnetic properties of cubic and hexagonal SrMnO3 are calculated using QuantumESPRESSO package within density functional theory in generalized gradient approximation GGA and GGA+U. The structural and electronic properties are obtained for several different possible magnetic configurations. In cubic and hexagonal cases the ground states show AF ordering. The GGA+U giving insulating properties paramagnetic and ferromagnetic for both phases better than GGA but in the cases of cubic ferromagnetic the system treats as half metallic properties. This half metallic property may be interesting in connection with spintronics devices if the hypothetical ferromagnetic configuration can be stabilized. The phonon result of ferromagnetic cubic SrMnO3 clearly indicates the presence of instability in the phases and a good indication of existent of other phases more sable than this cubic ferromagnetic phases.