Two-dimensional　(2D)　materials　have　been　demonstrated　to　be　ideal　candidates　to　design　high　performance　photodetector　owing　to　their　novel　optoelectronic　features.　However,　large　number　of　such　simple　photodetectors　are　photoconductive,　which　need　external　voltage　to　work　effectively.　In　this　paper,　we　proposed　a　kind　of　self-powered　photodetector　composed　of　semi-metallic　graphene,　semiconducting　MoSe2　and　Au　to　generate　two　asymmetric　contacts　because　these　three　materials　owns　different　work　functions.　On　one　hand,　the　open-circuit　voltage　between　MoSe2　and　Au　enables　the　device　to　achieve　self-powered　photodetection　with　the　high　responsivity　of　89.5　mA/W　and　specific　detectivity　of　2.24　x　10(10)　jones.　On　the　other　hand,　because　of　the　ohmic　contact　between　MoSe2　and　graphene,　electrons　can　be　transferred　rapidly　from　MoSe2　to　graphene,　leading　to　a　short　response　time　of　only　9.6　ms.　In　addition,　this　photodetector　possesses　broader　spectrum　detection　from　450　nm　to　900　nm　compared　with　the　one　made　by　MoS2　as　it　owns　much　narrower　bandgap.　Our　work　offers　a　new　approach　for　optoelectronic　device　design　with　low　power　consumption　but　high　responsivity.