Self-consistent periodic density functional theory (DFT) calculations were employed to explore the adsorption and reaction mechanisms of CO2 hydrogenation to methanol via the reverse water-gas-shift pathway on Cu(111) and three RhCu(111) surfaces with different doped-Rh atoms on Cu(111) surfaces, denoted as Rh3Cu6(111), Rh6Cu3(111) and Rh ML surfaces. All the possible favored adsorption sites, structures and adsorption energies of the relative species on Cu(111) and RhCu(111) were determined. H2CO*, HCO*, CO*, cis-COOH* and trans-COOH* adsorbing at Rh atoms through C atom are strengthened by the doped Rh, and the adsorption energies of species on Cu sites through O atom are not altered obviously, which can be explained by d-PDOS analysis. Through the analyses of Brønsted-Evans-Polanyi (BEP) relationships, it is found that the adsorption of trans-COOH* and co-adsorbed CO*/H* is stronger on RhCu(111) surfaces, while the energy of CO* in the TS geometry is dramatically decreased by doping with Rh atoms, leading to the alternation of rate-limiting step from CO2 hydrogenation forming trans-COOH* on Cu(111) and Rh3Cu6(111) surfaces to CO hydrogenation forming HCO* on Rh3Cu6(111) and Rh ML (monolayer) surfaces. The order of the highest activation barriers for the overall reaction is Cu(111) > Rh6Cu3(111) > Rh ML > Rh3Cu6(111). Moreover, due to the dissociative adsorption of H2, the yield of CO byproduct is suppressed. The calculated results show that the overall reaction process of CH3OH synthesis is facilitated kinetically and thermodynamically, especially on Rh3Cu6(111) surface. The present insights are helpful for the rational design and optimization of Rh-Cu bimetallic catalysts used in the process of CO2 hydrogenation to CH3OH synthesis.