Direct Methanol Fuel Cell (DMFC) have attracted attention in recent years because they are very energy-efficient. However, there is a serious problem in that Pt, which is the usual anode electrocatalyst, is poisoned by CO. Therefore, it is very important to develop new materials for use as electrocatalysts that exhibit good tolerance to CO. The aim of this study is to examine the mechanism of H2O dissociation and of the CO+OH combination reactions in the CO oxidation process by calculating the adsorption energies and the activation barriers. In the case of Pt-Ru alloys, the activation barrier for the H2O dissociation reaction is almost the same as it is for pure Pt. The activation barrier for the CO+OH combination reaction on the Pt-Ru alloy is larger than that on pure Pt. Nevertheless, the adsorption energy of H2O is larger than that on pure Pt. On the other hand, the activation barrier and adsorption energies of H2O on the Pt-Sn alloy are very close to the corresponding values on pure Pt. Moreover, the activation barrier for the CO+OH combination reaction on the Pt-Sn alloy is lower than that on pure Pt.