We investigate the pressure phase diagram of FeTe, predicting structural and magnetic properties in the normal state at zero temperature within density functional theory. We carefully examined several possible different crystal structures over a pressure range up to approximate to 30 GPa: simple tetragonal (PbO type), simple monoclinic, orthorhombic (MnP type), hexagonal (NiAs and wurzite type), and cubic (CsCl and NaCl type). We predict pressure to drive the system through different magnetic ordering (notably also some ferromagnetic phases), eventually suppressing magnetism at around 17 GPa. We speculate the ferromagnetic order to be the reason for the absence of a superconducting phase in FeTe at variance with the case of FeSe. DOI: 10.1103/PhysRevB.87.09451