Exploring　highly　efficient,　and　low-cost　oxygen　reduction　reaction　(ORR)　and　oxygen　evolution　reaction　(OER)　catalysts　is　extremely　vital　for　the　commercial　application　of　advanced　energy　storage　and　conversion　devices.　Herein,　a　series　of　graphene-like　C2N　supported　TMx@C2N,　(TM　=　Fe,　Co,　Ni,　and　Cu,　x　=　1,　2)　single-　and　dual-atom　catalysts　are　designed.　Their　catalytic　performance　is　systematically　evaluated　by　means　of　spin-polarized　density　functional　theory　(DFT)　computations　coupled　with　hydrogen　electrode　model.　Regulating　metal　atom　and　pairs　can　widely　tune　the　catalytic　performance.　The　most　promising　ORR/OER　bifunctional　activity　can　be　realized　on　Cu-2@C2N　with　lowest　overpotential　of　0.46　and　0.38　V　for　ORR　and　OER,　respectively.　Ni-2@C2N　and　Ni@C2N　can　also　exhibit　good　bifunctional　activity　through　effectively　balancing　the　adsorption　strength　of　intermediates.　The　correlation　of　reaction　overpotential　with　adsorption　free　energy　is　well　established　to　track　the　activity　and　reveal　the　activity　origin,　indicating　that　catalytic　activity　is　intrinsically　governed　by　the　adsorption　strength　of　reaction　intermediates.　The　key　to　achieve　high　catalytic　activity　is　to　effectively　balance　the　adsorption　of　multiple　reactive　intermediates　by　means　of　the　synergetic　effect　of　suitably　screened　bimetal　atoms.　Our　results　also　demonstrate　that　lattice　strain　can　effectively　regulate　the　adsorption　free　energies　of　reaction　intermediates,　regarding　it　as　an　efficient　strategy　to　tune　ORR/OER　activity.　This　study　could　provide　a　significant　guidance　for　the　discovery　and　design　of　highly　active　noble-metal-free　carbon-based　ORR/OER　catalysts.