The promoter metal monolayer deposited over other metal substrate exhibits excellent catalytic performance, in this study, the mechanism of syngas conversion to C-2 oxygenates over the promoter M(M = Rh, Co) monolayer-modified Cu catalysts have been systematically investigated to identify the role of monolayer promoter M and its effect on the selectivity using density functional theory calculations. Here, two key steps are examined, including the formation of key CHx intermediates and the C-C bond formation of C-2 oxygenates. The results show that compared to the pure Cu catalyst, the promoter Co monolayer-modified Cu catalyst exhibits higher selectivity towards CHx(x = 1-3) formation instead of methanol, the most favored CHx monomer is CH2; whereas CHx(x = 1,2) is the most favored CHx monomer on the promoter Rh monolayer-modified Cu(111), which is competitive with methanol formation. The favored CHx monomer originates from the C-O bond cleavage of CHxO(x = 1,2) and CHxOH(x = 1,2) species formed by CO hydrogenation. Starting from the favored CHx monomer, compared to the pure Cu catalyst, C-2 oxygenates formed by CHO insertion into CHx is the most favorable over the promoter Rh and Co monolayer-modified Cu catalysts. In general, the promoter Co monolayer-modified Cu catalyst exhibits higher selectivity towards syngas conversion to C-2 oxygenates than the promoter Rh monolayer-modified Cu, as well as the pure Cu, Rh and Co catalysts, the reasons is attributed to that the d-band center of Co monolayer-modified Cu is the closest to Fermi level leading to the enhancement of adsorption capacity of the intermediates, and promoting the C-O bond activation as well as reducing the repulsion interaction between CHx and CHO to facilitate the formation of C-2 oxygenates. The present study provides useful information for the design of highly efficient catalysts with the metal promoter monolayer-modified metal substrate in syngas conversion to C-2 oxygenates.