Methanol synthesis from CO₂ hydrogenation catalyzed by Zn/Cu alloy has been widely studied, but there is still debate on its catalytic active phase and whether the Zn can be oxidized during the reaction process. What is more, as Zn atoms could locate on Zn/Cu alloy surface in forms of both single atom and cluster, how Zn surface distribution affects catalytic activity is still not clear. In this work, we performed a systematic theoretical study to compare the mechanistic natures and catalytic pathways between Zn single atom and small cluster on catalyst surface, where the surface oxidation was shown to play the critical role. Before surface oxidation, the Zn single atom/Cu is more active than the Zn small cluster/Cu, but its surface oxidation is difficult to take place. Instead, after the easy surface oxidation by CO₂ decomposition, the oxidized Zn small cluster/Cu becomes much more active, which even exceeds the hardly-oxidized Zn single atom/Cu becoming the active phase. Further analyses show such dramatic promotion of surface oxidation can be ascribed to the following factors: i) The O from surface oxidation could preferably occupy the strongest binding sites on the center of Zn cluster. That makes the O intermediates bind at the Zn/Cu interface, preventing their too tight binding for further hydrogenation; ii) The higher positive charge and work function on the oxidized surface could also promote the hydrogenation of O intermediates. This work provided one more example that under certain condition, the metal cluster can be active than the single atom in heterogeneous catalysis.