The　structural,　elastic　and　electronic　properties　of　Co7M6　(M　=　W,　Mo,　Nb)　mu　phases　were　investigated　by　first-principles　calculations　based　on　the　density　functional　theory　(DFT).　The　calculated　cohesive　energy　indicates　that　Co7M6　(M　=　W,　Mo,　Nb)　mu　phases　are　thermodynamically　stable.　Besides,　Co7W6　owns　a　higher　structural　stability　than　that　of　Co7Mo6　and　Co7Nb6.　The　obtained　elastic　constant　demonstrates　that　Co7M6　(M　=　W,　Mo,　Nb)　are　mechanically　stable.　With　Voigt-Reuss-Hill　(VRH)　approximation,　the　elastic　bulk　modulus　(B),　shear　modulus　(G),　Young＇s　modulus　(E)　and　Poisson＇s　ratio　(nu)　were　derived.　The　ductility　and　plasticity　as　well　as　the　elastic　anisotropy　of　the　three　phases　were　discussed　in　details.　Finally,　the　density　of　states　and　charge　density　difference　were　also　analysed　to　reveal　the　underlying　mechanism　of　structural　stability　and　the　elastic　properties.