The structural stabilities, elastic, electronic and magnetic properties of the Heusler-type shape memory alloy Ni2FeGa are calculated using density functional theory. The volume conserving tetragonal distortion of the austenite Ni2FeGa find an energy minimum at c/a = 1.33. Metastable behaviour of the high temperature cubic austenite phase is predicted due to elastic softening in the [110] direction. Calculations of the total and partial magnetic moments show a dominant contribution from Fe atoms of the alloy. The calculated density of states shows a depression in the minority spin channel of the cubic Ni2FeGa just above the Fermi level which gets partially filled up in the tetragonal phase. In contrast to Ni2MnGa, the transition metal spin-down states show partial hybridization in Ni2FeGa and there is a relatively high electron density of states near the Fermi level in both phases.