Two-dimensional　monolayer　C3N　has　attracted　much　attention　in　many　fields,　owing　to　its　unique　mechanical,　electrical　and　thermal　properties　and　diverse　structure.　However,　the　physical　origin　of　these　properties　lacks　a　systematic　and　clear　understanding.　In　this　work,　three　dynamically　stable　metallic　C3N　allotropes　were　computationally　investigated.　The　cohesive　energy　of　all　these　structures　is　within　0.09　eV/atom　of　that　of　the　experimentally　reported　semi-conductive　C3N　structure.　Density-functional　theory　calculations　showed　that　the　metallicity　of　two-dimensional　C3N　can　be　attributed　to　the　continuity　of　the　carbon　chains,　which　form　channels　for　passage　of　free　electrons.　Furthermore,　additional　calculations　showed　that　the　C3N　allotropes　possess　excellent　mechanical　properties,　good　electronic　conductivity　and　Li　migration　capability　(wherein　the　C-C　chains　provide　a　good　migration　channel　for　lithium　ions).　These　properties　make　C3N　a　promising　candidate　for　Li-ion　battery　anode　materials.　Our　findings　suggest　a　physical　mechanistic　basis　for　modulating　the　electrochemical　properties　of　such　materials　by　controlling　the　arrangement　of　atoms.　The　study　also　provides　new　ideas　for　the　modulation　of　the　structure　and　properties　of　two-dimensional　materials　and　points　out　a　direction　for　the　ongoing　development　and　application　of　C-N　materials　and　devices.