Calculations of adsorption and reaction mechanism on ZnO surface have been investigated. In this work, the deposition of six atomic copper clusters (6Cu) on ZnO surface (called 6Cu/ZnO model), using density functional theory was employed to calculate for CO and H2O co-adsorption. In performance, on ZnO surface, 6Cu were adsorbed to obtain four stable sites of 6Cu/ZnO model, called as 6Cu-I, 6Cu-II, 6Cu-III, and 6Cu-IV. The calculated results found that the 6Cu-IV was the most stable surface model, thus, used to examine the co-adsorption of CO and H2O molecules. Further, CO and H2O co-adsorption on ZnO surface were calculated also to compare with 6Cu/ZnO surface. Based on co-adsorption energy calculations indicated that CO and H2O co-adsorption on 6Cu/ZnO surface were more favorable than on ZnO surface. The studied results will provide an insight into the effective adsorption of cluster on ZnO-based surface by deposition.