The mechanism of CO oxidation by O2 on Au atoms supported on the pristine and defected hexagonal boron nitride (h-BN) surface has been studied theoretically using density functional theory. Two possible routes for catalytic oxidation are considered. The first route consists in a preliminary dissociation of the adsorbed O2 followed by consequential oxidation of a reactant molecule by atomic oxygen. Although the presence of h-BN surface can change the O2 dissociation barrier, it remains relatively high. The second route is a direct oxidation reaction between the activated molecular oxygen and the reactant. We have found two different pathways for CO oxidation: a two-step pathway where two CO2 molecules are formed independently, and a self-promotion pathway where oxidation of the first CO molecule is promoted by the second CO molecule. Interaction of Au with the defect-free and defected h-BN surface considerably affects the CO oxidation reaction pathways and barriers. Therefore, Au supported on the h-BN surface (pristine or defected) cannot be considered as pseudo-free atom and support effects have to be taken into account, even when the interaction of Au with the support is weak.