The atomic ordering, electronic structure, magnetic properties and martensitic transformation of three new all-d-metal Heusler alloys Mn2PtZ (Z = Sc, Ti and V) have been investigated theoretically to discover new magnetic shape memory alloys (MSMAs). Depending on the different third transition metal element Z, Mn2PtSc and Mn2PtTi tend to form XA structure while Mn2PtV forms L21 structure. This difference is related to their DOS structures. Charge density difference calculations indicate enhanced d-d hybridization in these all-d-metal Heusler alloys. Mn2PtZ are all ferrimagnets with their Mn-Mn or Mn-V local spin moments antiparallel coupled. In these alloys, Mn2PtTi is a possible new MSMA with the energy difference ΔEM between the martensite and austenite as large as −262 meV/f.u., which indicates a high martensitic transformation temperature and is related to the Jahn-Teller effect in the electronic structure. A large volume effect of 2.9% cell shrinkage occurs during the martensitic transformation. All this makes Mn2PtTi a promising candidate for MSMAs with wide applications.