Tetragonal distortion of Mn2NiGa Heusler alloy is calculated by first-principles based on density functional theory with projector augmented wave pseudopotential, and the magnetism, electronic structure, elastic constants and phonon frequencies are also calculated and analyzed. The contribution of the spin magnetic moments of Mn atom to the total moment is largest for Mn2NiGa, and the Mn2NiGa alloy shows ferrimagnetism in these two cases, owning to the antiparallel but unbalanced magnetic moments of Mn (A) atom and Mn (B) atom. Analysis of tetragonal distortion shows that there is a local minimum total energy at c/a=0.94 and c/a=1.27, which corresponds to a stable martensitic phase. Elastic constants of Mn2NiGa reveal that cubic structure does not satisfy stability conditions, but tetragonal structure (c/a=0.94 and c/a=1.27) does. The imaginary values of phonon frequencies in cubic structures validate that tetragonal structure (c/a=0.94 and c/a=1.27) of Mn2NiGa is more stable than cubic structure. The phase transition temperature of c/a=1.27 tetragonal structure converting to cubic structure is about 315 K.