Density functional theory (DFT) calculations were used to study C-2 oxygenate from syngas over bimetallic Co/Cu catalysts. The thermodynamics and kinetics for all possible elementary steps involved in the formation of C-2 oxygenate from syngas have been investigated on both pure and Cu-doped Co(0001) surfaces. By comparing the results on two surfaces, the role of copper in improving the selectivity toward C-2 oxygenates has been identified as two aspects: (1) controlling the Co ensemble size and blocking the active sites for C-O bond cleavage, which results in inhibition of CHx coupling to hydrocarbons; (2) providing undissociated CO/HCO as well as reducing the barriers for HCO insertion toward the formation of oxygenate precursors. With the combination of the mechanistic study and the charge analysis on the bimetallic surface, we conclude that the nature of the copper promotion is mainly a geometric effect rather than an electronic effect.