By means of density functional theory, the adsorption properties of O₂ molecule on both isolated and N-graphene supported gold clusters have been studied. The N-graphene is modeled by a C₆₅NH₂₂ cluster of finite size. The results indicate that the catalytic activity and the O₂ adsorption energies of odd-numbered Au clusters are larger than those of adjacent even-numbered ones. The O₂ molecule is in favor of bonding to the bridge sites of odd-numbered Au clusters, whereas for odd-numbered ones, the end-on adsorption mode is favored. The perpendicular adsorption orientation on N-graphene is preferred than the parallel one for Au₂, Au₃ and Au₄ clusters, while for Au₅, Au₆ and Au₇, the parallel ones are favored. When O₂ is adsorbed on N-graphene supported Au clusters, the adsorption energies are largely increased compared with those on gas-phase ones. The increased adsorption energies would significantly facilitate the electron transfer from Au d-orbital to π* orbital of O₂, which would further weakening the O-O bond and therefore enhancing the catalytic activity. The carbon atoms on N-graphene could anchor the clusters, which could make them more difficult to structural distortion, therefore enhance their stability.