The spin-gapless semiconductors with parabolic energy dispersions [1–3] have been recently proposed as a new class of materials for potential applications in spintronic devices. In this work, according to the Slater-Pauling rule, we report the fully-compensated ferrimagnetic (FCF) behavior and spin-gapless semiconducting (SGS) properties for a new inverse Heusler compound Zr 2 MnGa by means of the plane-wave pseudo-potential method based on density functional theory. With the help of GGA-PBE, the electronic structures and the magnetism of Zr 2 MnGa compound at its equilibrium and strained lattice constants are systematically studied. The calculated results show that the Zr 2 MnGa is a new SGS at its equilibrium lattice constant: there is an energy gap between the conduction and valence bands for both the majority and minority electrons, while there is no gap between the majority electrons in the valence band and the minority electrons in the conduction band. Remarkably, not only a diverse physical nature tra nsition, but also different types of spin-gapless features can be observed with the change of the lattice constants. Our calculated results of Zr 2 MnGa compound indicate that this material has great application potential in spintronic devices.