The oxidation of the TiC(001) surface by O-2 has been investigated by using density functional theory with a slab model. The geometrical optimizations and band structure calculations have been performed for several possible oxygen-adsorbed models. Our results show that the O-2 molecule tends to be adsorbed dissociatively on an atop site of the surface carbon atoms, but the pattern of oxygen atom bonded to the surface metal site is most unfavorable. This selective oxidation of the surface can be explained well by considering the component of the surface states of TiC(001), and the dominant 2P(z) character of the surface C atom found in the surface states is responsible for the surface chemistry of the TiC(001) surface. When the oxygen atom is bonded to surface C atom, the predicted results including the difference density of state, variation of work function and the surface core level shifts are in good agreement with the experimental measurements. In the calculated reaction pathway, a molecular precursor is observed and there is no energy barrier to dissociative adsorption of O-2 on the TiC(001) surface. Furthermore, a method based on the decomposition of the energy band is presented in this work to describe the band structure of TiC(001) surface on exposure to O-2.