In　our　study,　DFT　calculations　were　employed　to　study　the　influence　of　both　adsorbed　H2　and　H2O　upon　the　catalysis　reactivity　of　CO2　hydrogenation　to　methanol　over　two　exposed　planes　of　In-Rh　alloy.　For　InRh(011),　CH3OH　formation　is　not　viable　from　both　＂Formate＂　and　＂RWGS+CO-Hydro＂　mechanisms　owing　to　the　substantial　kinetic　barrier　encountered.　For　In3Rh(212),　the　activated　H*　prefers　to　adsorb　at　surface　Rh　atoms　from　the　first　layer　and　thereby　generates　three　potentially　reactive　sites　(Rh_I,　Rh_II　and　Rh_III),　from　which　methanol　is　produced　through　the　＂Formate＂　pathway.　Based　on　the　microkinetic　model,　methanol　is　selectively　produced　from　Rh_III　while　CO　is　the　favorable　product　from　the　other　two.　Methanol　formation　from　both　Rh_I　and　Rh_II　is　substantially　limited　by　the　rate-determining　step　(RDS)　owing　to　the　bridging　configuration　of　H*　being　too　stable.　As　a　major　side　product　of　CO2　hydrogenation,　H2O　introduction　could　lower　the　RDS　of　the　＂Formate＂　pathway　from　Rh_III　and　thereby　substantially　improve　its　production　rate　of　methanol.　Overall,　our　calculation　determines　the　reactive　site　of　In-Rh　alloy　and　explains　the　way　how　H2　and　H2O　influence　the　reaction　mechanism　and　catalysis　performance　of　the　bimetallic　system.