By　means　of　density　functional　theory,　the　adsorption　properties　of　O-2　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　O-2　adsorption　energies　of　odd-numbered　Au　clusters　are　larger　than　those　of　adjacent　even-numbered　ones.　The　O-2　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　Au-2,　Au-3　and　Au-4　clusters,　while　for　Au-5,　Au-6　and　Au-7,　the　parallel　ones　are　favored.　When　O-2　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　pi*　orbital　of　O-2,　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.