First-principles　calculations　were　performed　to　explore　the　detailed　reaction　mechanisms　of　CO2　conversion　to　methanol　over　two　size-selected　copper　clusters　supported　on　the　TiC(001)　surface,　in　which　three　potential　routes　including　the　formate,　the　reverse　water-gas-shift　(RWGS)　+　CO-hydrogenation,　and　the　C-O　bond　cleavage　pathways　were　considered.　Our　findings　show　that　the　adsorption　and　migration　of　hydrogen　atoms　have　obvious　impact　on　the　catalytic　activity　for　CO2　conversion.　The　limited　size　of　the　active　site　of　small　Cu　cluster　with　a　planar　configuration　results　in　that　the　formate　route　is　difficult　to　occur　because　the　creation　of　H2COOH*　intermediate　requires　the　spillover　of　H　atoms　from　the　substrate　to　the　active　center　by　overcoming　a　high　kinetic　barrier.　On　the　contrary,　the　polyhedron　structure　in　the　large　Cu　cluster　can　act　as　a　reservoir　for　the　hydrogen　adsorption,　making　it　possible　to　produce　methanol　via　the　formate　pathway.　Although　the　RWGS　+　CO-hydrogenation　pathway　is　identified　as　the　preferred　reaction　pathway　on　both　surfaces,　the　relatively　strong　binding　of　hydrogen　on　the　large　copper　cluster　causes　difficulty　in　the　migration　of　H　toward　the　reaction　intermediate.　The　results　of　microkinetic　simulations　indicate　that　the　rate-limiting　steps　are　sensitive　to　cluster　size,　and　small　Cu　cluster　exhibits　better　catalytic　activity　for　the　conversion　of　CO2　to　CH3OH.