In order to reduce the amount and cost of gold catalyst in practical application, it is an effective technical strategy to construct binary metal alloy with gold and transition metals. In this work, the adsorption behaviors and dissociation reaction path of water on the different surfaces of Au, Cu, and AuCu binary alloy were studied by using DFT calculations. Based on the calculations, the corresponding catalytic performance of each model was further analyzed. The calculated results showed that the catalytic activity of the considered four surface models is on the following order: Au(111) < AuCu(111)-Cu < AuCu(111)-Au < Cu(111), if using the active energy as comparison standard. The underlying reason of this phenomenon is closely related with the adsorption behavior: the molecular adsorptions of water on Cu(111) and AuCu(111)-Au surfaces have relatively small adsorption energies; while at the same time, the dissociation adsorptions of water on these two surfaces have relatively large adsorption energies. Based on the electron transfer and bonding electronic structure, it could be found that the more electrons transfer between surface and water or H+OH groups, the more strong interaction between catalyst and adsorbate. Furthermore, the overlapping or hybridization between the d states of metal atoms on the surface and the 1b₁ states of water or lb₁-like states of H+OH groups also determines this interaction. Therefore, using AuCu binary alloy to replace Au as catalyst or co-catalyst reduces cost, and enhances the catalytic activity.