Recent experiential and theoretical studies have shown that the Ag-Cu bimetallic catalysts possess a high selectivity toward ethylene oxide (EO) in ethylene epoxidation. However, the dependence of selectivity toward EO on Ag-Cu composition remains unclear. In this work, a volcano-like selectivity trend with the increasing surface Cu content (x) of Ag1-xCux/Ag (111) surface alloy has been identified by density functional theory (DFT) calculations. The computational screening demonstrates that the Ag1-xCux/Ag (111) surface alloy would achieve the highest selectivity with around 50% surface Cu composition at 1/9 and 2/9 ML oxygen coverage. We find that the relative bond strength between the C-1-O and O-metal bonds in the oxametallacycle (OMC) intermediate would affect the selectivity to EO. Moreover, the transition state, the charge distribution of the Ag-Cu surfaces, and the changes in work function of catalysts upon adsorption of O-s are studied, which also to some extent affect the selectivity.