We have investigated the dissociative adsorption process of O2 (oxygen molecule) on a composite surface formed by coating a single platinum (Pt) adatom on a gamma-alumina (\gamma-Al2O3) (111) surface. This process is studied by using density functional theory (DFT) and described in terms of potential energy surfaces (PES) with respect to the molecular degrees of freedom. We compare the activation barriers and adsorption energies among typical reaction channels. Our results show that O2 dissociative adsorption is preferably occurred when this O2 molecule approaches the surface with molecular orientation inclined by 30° angle with respect to the surface normal, i.e., the condition with lowest activation barrier. The results indicate that dissociated O atoms are likely to form strong bonds with the Pt adatom by keeping distance from the alumina layer.