The　electronic　structures　of　MC　compounds　(M　=　3d　transition　metal)　in　NaCl　CsCl　and　WC　phases　have　been　investigated　by　using　the　first　principle　method.　The　calculated　results　indicate　that　the　band　structures　of　the　MC　compounds　in　the　same　phase　are　similar,　and　as　a　result　of　the　rigid　band　model,　we　obtained　the　uniform　distribution　of　the　density　of　states　(DOS)　for　MC　compounds　in　three　phases.　According　to　the　DOS　value　near　the　Fermi　level　and　the　calculated　cohesive　energy,　the　relative　stability　for　three　phases　can　be　determined.　For　the　MC　compounds　in　CsCl　phase,　it　exhibits　the　bad　phase　stability.　For　the　MC　compounds　of　Se　similar　to　V,　the　most　stable　phase　is　NaCl　phase,　and　the　WC　phase　is　suitable　for　the　MC　compounds　of　Cr　similar　to　Ni.　Moreover,　the　chemical　bonding　of　MC　compounds　in　three　phases　has　been　studied　by　using　the　two-sublattice　model,　and　their　influences　on　the　phase　stability　are　also　discussed.