To understand the catalytic activity of Ag-Cu cluster as catalyst of ethylene oxidation, bare Ag and Cu and Ag core/Cu12 shell and Cu core/Ag12 shell are built and optimized by density functional theory calculations incorporating the effect of the atmospheric environment. Consequently different oxygen adsorption sites on the cluster are considered: top site of the shell atoms, bridge site of the shell atoms and hollow site of the shell atoms. For each adsorption site, a few coverages are considered, both oxygen-rich condition and oxygen-poor condition. The phase diagrams of oxygen and 13-atom Ag-Cu clusters are finally determined. The pressure-temperature phase diagrams are determined for the oxygen and 13-atom Ag-Cu clusters, which reveal important insights into this system and its catalytic properties. The phase diagrams of oxygen and 13-atom Ag-Cu clusters are finally determined. The results predict the most stable phase: structure and adsorption of oxygen at certain temperature and certain pressure. Under oxygen-poor condition, the cluster structures are most likely to be changed. This information must be helpful to understand the catalytic process of Ag-Cu cluster as catalyst of ethylene oxidation.