The　electrochemical　properties　of　g-CN　and　g-CN/graphene　heterostructure　as　anode　materials　for　lithium-ion　batteries　were　investigated　by　density　functional　calculations.　It　is　shown　that　the　Li　adsorbed　in　the　pore　of　g-CN　has　strong　interactions　with　g-CN　and　a　high　diffusion　energy　barrier,　leading　to　Li　being　trapped　in　the　pores.　After　the　pores　of　g-CN　are　fully　adsorbed　(C3N3Li),　the　migration　energy　barrier　of　Li　ion　on　the　surface　of　C3N3Li　decreased　to　0.56　eV.　The　calculated　capacity　(197　mAh/g)　using　C3N3Li　as　the　host　system　is　in　agreement　with　experiment　results.　Similarly,　the　adsorption　energy　of　Li　in　the　pore　of　g-CN　in　the　g-CN/　graphene　heterostructure　is　-　2.74　eV　and　the　diffusion　energy　barrier　(2.44　eV)　for　Li　ion　is　still　too　high　to　migrate　in　the　adjacent　pores.　Therefore,　C3N3Li/graphene　was　used　as　the　host　anode　system,　and　suitable　adsorption　energies　(-0.81　eV),　low　migration　energy　barrier　(0.43　eV),　and　a　capacity　of　694　mAh/g　were　obtained,　which　suggests　that　C3N3Li/graphene　can　be　a　promising　anode　material　for　Li-ion　battery.