The　adsorption　and　hydrogenation　of　carbon　dioxide　on　γ-Al2O3(110)　surface-supported　copper　clusters　of　different　sizes　are　investigated　using　density　functional　theory　calculations.　Our　results　show　that　the　activation　of　CO2　is　most　obvious　at　the　Cu/γ-Al2O3　interface　containing　the　size-selected　Cu4　cluster.　It　is　interesting　that　the　CO2　activation　is　more　pronounced　at　the　partially　hydroxyl-covered　interface.　The　catalytic　mechanisms　of　CO2　conversion　to　methanol　at　the　dry　and　hydroxylated　Cu4/γ-Al2O3　interfaces　via　the　formate　route　and　the　pathway　initiated　through　the　hydrogenation　of　carbon　monoxide　produced　by　the　reverse　water–gas　shift　reaction　are　further　explored.　On　both　interfaces,　the　formate　pathway　is　identified　as　the　preferred　reaction　pathway,　in　which　the　hydrogenation　of　HCOO　to　H2COO　is　the　rate-limiting　step　(RLS).　However,　since　the　surface　OH　group　can　act　as　a　hydrogen　source　in　some　elementary　reactions,　unlike　the　dry　surface,　the　production　of　H2COOH　species　along　the　formate　pathway　is　found　at　the　hydroxylated　interface.　In　addition,　the　introduction　of　OH　at　the　interface　leads　to　an　increase　in　the　kinetic　barrier　of　the　RLS,　indicating　that　surface　hydroxylation　has　a　negative　effect　on　the　catalytic　activity　of　CO2　conversion　to　CH3OH　at　the　Cu/γ-Al2O3　interface.　©　2023　by　the　authors.