First-principles calculations are performed to investigate pressure effects on structure, magnetism, martensitic phase transition and Curie temperatures of Mn2PtGa Heusler alloy in framework of the density functional theory. It is shown that Mn2PtGa prefer to crystallize in the inverse Heusler type structure. Besides, we predict an extraordinary occurrence of pressure induced metallic ferrimagnetism to half-metallic ferromagnetism transition in cubic phase of Mn2PtGa alloy under hydrostatic pressure up to 43 GPa and the half-metallic ferromagnetism is found to be robust even the lattice further compression to 90 GPa. However, with the pressure up to 100 GPa, the spin-down gap starts to close and the half metallicity begin to disappear, while with the pressure increasing from 100 GPa to 300 GPa, the alloy returns to metallic characteristic. In addition, the energy difference between the austenitic and martensitic phases is found to increase with increasing pressure followed by a decrease when pressure reaches to 43 GPa, which implies a variation trend of martensitic phase transition temperature. Furthermore, Curie temperatures in both austenitic and martensitic phases are estimated under pressure by using the standard mean-field approximation which agrees well with the theoretical results in literature. The robustness of the half metallicity, magnetic transition and the high Curie temperature under pressure make Mn2PtGa alloy a promising candidate for applications in spintronic devices.