Geometry, formation, electronic structure as well as magnetic properties of the tetragonal MnGa alloy were systematically studied by density functional theory method. The results show that the tetragonal MnGa has formation enthalpy of -4.85 eV, which is slightly higher than other compounds without d state electrons. It has conductor like band structure with the deep valance bands formed by d state electrons, they show strong localization effect. The tetragonal MnGa alloy shows obvious spin polarization. The s state electrons near Fermi energy and the p state electrons under Fermi energy have weak spin polarization, the d state electrons which form conductor band and bands below Fermi energy have strong spin polarization, they contribute to the total electronic as well as magnetic properties. The s and p state electrons of Mn have weak spin polarization, its d electrons which form conductor band and bands below Fermi energy have strongest spin polarization. The d electrons of Ga which form bands below Fermi energy have weak spin polarization. The two kinds of Ga have different spin polarization states. The tetragonal MnGa alloy has net magnetic moment, it shows weak ferrimagnetism.