Density functional theory calculations (DFT) were performed to study reactions on the uranium monocarbide (UC) surface when it is in contact with O atoms and O2 molecules. By studying the effects of the effective Hubbard parameter, Ueff, on surface energy, adsorption energy and work function, we identify that the conventional GGA method can give relatively reasonable results for surface systems. For the adsorption of O atom, it's found that the O atom prefers to be adsorbed at the hollow site for 1 and 0.5 monolayers (ML); however, the O atom tends to be adsorbed atop the U atom rather than the hollow site for 0.25 ML. We investigate the impact of coverages on surface adsorption using ab initio thermodynamics. The diffusion properties of O atoms on the surface are completely different according to different diffusion paths. As for O2, the surface adsorption of the O2 atop the U atom is non-dissociated for all horizontal and vertical adsorption approaches, but O2 prefers to dissociate into two O atoms for other sites. The analysis of charge density difference shows that O atoms only react with atoms on the surface and subsurface of UC. Co-adsorption studies on surfaces have shown that O atoms on the surface can hinder the chemisorption behavior of OH− while promoting the physical adsorption of water molecules on the surface.