Poly(N-vinyl-2-pyrrolidone) (PVP) is often used to protect active Au clusters from coalescence. The influences of PVP on the O₂ adsorption on Au₃₂ clusters were investigated using density functional theory calculations. Various low-lying structures of O₂:Au₃₂ and O₂:Au₃₂:PVP complexes, in which the Au₃₂ is either neutral or anionic and the O₂ is either molecular or dissociative, were identified. The PVP influences were evaluated in terms of the changes in geometry, adsorption energy, charge redistribution, spin density, and density of states upon PVP pre-adsorption. Our calculations reveal that PVP weakly adsorbs on the cluster surface, with rather small changes in the structural, geometrical and electronic properties that are relevant to the O₂ activation. The activity of neutral or anionic Au₃₂ towards O₂ is kept or slightly enhanced by PVP because of the cooperative adsorption of PVP and O₂. This is the structural basis of choosing PVP as the protective ligand for Au clusters.