High　efficiency　and　wide　bandwidth　are　the　main　optimization　directions　for　energy　harvester.　Based　on　flexoelectric　theory,　this　paper　presents　a　micro　cantilever　vibration　energy　harvester　(VEH)　with　a　broad　bandwidth　which　achieved　by　collisions　of　two　beams.　The　nanocrystalline　graphene　(NCG)　is　selected　as　base　layer　because　its　quality　factor　(Q　factor)　is　highest　compared　with　common　materials,　which　means　its　energy　loss　in　progress　of　power　conversion　is　lowest　and　device　has　a　high　sensitivity　to　external　excitation.　Considering　flexoelectric　effect,　based　on　Hamilton＇s　principle　and　Hertz　contact　force　model,　the　electromechanical　coupling　equations　are　obtained.　Numerical　simulations　are　conducted.　Output　voltages　of　upper　and　lower　beam　are　calculated　respectively　and　the　frequency　response　curve　of　the　power　density　is　obtained.　It　has　been　found　that　the　maximum　output　voltage　of　flexoelectric　energy　harvester　is　almost　5　times　that　of　piezoelectric　energy　harvester　when　the　thickness　of　substrate　layer　is　400　nm.　The　effects　of　some　parameters,　such　as　resistance,　gap　distance　between　two　beams,　and　tip　mass,　on　the　performance　of　harvester　are　studied.　It　indicates　that　the　working　bandwidth　of　the　VEH　has　increased　approximately　fourfold,　and　the　output　power　density　is　improved　in　some　case　due　to　collision　of　two　beams,　which　has　been　verified　by　experiment.　This　work　designs　a　novel　efficient　micro　VEH　and　provides　a　theoretical　basis　for　structure　optimization.　©　2021　Elsevier　Ltd