Mn2CrGa　is　a　newly　found　Heusler　compound　with　most　of　its　properties　remain　unknown.　We　investigated　this　system　using　first-principles　calculation　and　found　that　it　can　show　a　martensitic　transformation　with　a　highly　ordered　L2(1)　structure.　However,　the　experimental　results　of　melt-spun　Mn2CrGa　ribbons　show　a　disordered　A2-type　structure　which　tends　to　decompose　into　D0(19)　and　D0(3)-type　phases　during　annealing.　These　characters　prohibit　the　predicted　martensitic　transformation　from　happening.　This　system　also　shows　interesting　features　like　relatively　high　Curie　temperature　and　strong　magnetic　interactions,　which　deserve　further　studies.