The CO oxidation on the Au(321) surface was investigated using spin polarized density functional theory based calculations within the GGA-PW91 exchange-correlation functional. This was done by studying separately the adsorption of isolated CO or CO2 and also the coadsorption of CO + O or CO + O-2 on the Au(321) surface. A periodic supercell approach was used to model the gold surface. The kinetic profile of the oxidation reaction was determined with the climbing image-nudged elastic band method and also with the dimer approach. It was found that CO adsorbs on the clean surface preferably at the kinks, and the same preference exists if atomic or molecular oxygen is coadsorbed on the Au(321) surface. CO2 is weakly adsorbed on Au(321) and appears at large distance from the metal surface. Importantly, the formation of carbonate species or of four atoms compounds, OCOO, adsorbed on the Au(321) surface is thermodynamically favorable from CO and O-2. The reaction of CO oxidation by atomic oxygen occurs almost without any energy cost on a reconstructed surface, whereas moderate barriers of similar to 0.6 eV were computed for the direct reaction with molecular oxygen occurring at the surface steps. These results suggest that the predissociation of the molecular oxygen on the Au(321) surface for the CO oxidation is energetically less favorable than the direct reaction with molecular oxygen. Finally, the products of the oxidation reaction are much more stable than the four atoms compound.