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Recently, 50-nm Heusler Mn3Al thin films were experimentally synthesized by Jamer et al. [Phys. Rev. Appl. (2017), 7, 064036] and the nominal zero moment, i.e. the fully compensated ferrimagnetic property, of these thin films was confirmed. That work motivated the current investigation on the martensitic transformation, electronic structure and magnetism of D03-ordered Mn3Al using first-principles calculations. Owing to tetragonal distortion, the martensitic transformation only occurs with tensile strain rather than with compressive strain and the half-metallic-type Mn3Al becomes a magnetic metal. Consequently, Mn3Al shows great potential for application as a ferromagnetic shape memory alloy. Moreover, not only did the martensitic transformation occur in Mn3Al, it was also observed in similar D03-ordered Mn3Z (Z = B, Ga, Ge, Sb) compounds.