We　perform　first-principles　calculations　to　investigate　whether　or　not　nitrogen　is　the　best　dopant　in　system　of　Co-X-4　embedded　graphene　(X=N,　S,　B,　and　P)　electrocatalysts　towards　hydrogen　evolution　reaction(HER).　Our　theoretical　results　reveal　that　N,　S,　B,　and　P-doped　graphene　can　enhance　the　catalytic　activity　toward　HER　compared　with　the　pristine　graphene,　and　S　doped　graphene　exhibits　more　favorable　performance　than　N　doped　graphene,　consistent　with　the　experimental　results.　For　the　Co-X-4　embedded　graphene　(X=N,　S,　B,　and　P),　we　predict　that　S　may　be　a　promising　dopant　in　graphene　supported　single　atom　Co.　The　rather　low　hydrogen　adsorption　free　energy　(-0.07　eV)　and　activation　energy　barrier　(0.78　eV)　for　the　rate-determining　step,　the　downshift　of　the　d　band　center,　the　enhanced　charge　density　of　d(z)(2)　orbital　as　well　as　the　reduced　work　function　are　responsible　for　the　unexpected　activity　of　Co-S-4　embedded　graphene　for　HER.　Overall,　Co-S-4　embedded　graphene　catalyst　could　be　a　good　candidate　for　hydrogen　evolution　reaction.