Diffusion Monte Carlo (DMC) calculations were performed for an accurate description of the nature of the O 2 adsorption on a single layer graphene. We investigated the stable orientation of O 2 at a specific adsorption site as well as its equilibrium adsorption energy. At equilibrium adsorption distances, an O 2 molecule was found to prefer a horizontal orientation, where the O-O bond is parallel to the graphene surface, to the vertical orientation. However, the vertical orientation is favored at the O 2 -graphene distances shorter than the equilibrium distance, which could be understood by the steric repulsion between O and C atoms. Contrary to previous DFT calculations, our DMC calculations show that the midpoint of a C-C bond (a bridge site) is energetically preferred for the O 2 adsorption to a center of a hexagonal ring (a hollow site). The lowest DMC adsorption energy was found at an intermediate point between a hollow and a bridge site, where the O 2 adsorption energy was estimated to be −0.142(4) eV that was in very good agreement with the recently-reported experimental value. Finally, we have found that O 2 is very diffusive on the surface of graphene with the diffusion barrier along a bridge-hollow-bridge path being as small as ∼ 11 meV.