Density　functional　theory　calculations　were　carried　out　to　investigate　the　mechanism　of　CO2　and　CO　methanation　over　pure　Cu(100)　and　Co-Cu　bimetallic　catalysts.　The　most　favorable　pathways　for　the　CO2　and　CO　hydrogenation　were　obtained.　For　the　Cu(100)　surface,　the　barriers　of　the　rate-limiting　step　for　the　HCOO*　and　CO*　hydrogenation　were　122.52　kJ/mol　and　106.14　kJ/mol.　Because　the　barrier　(77.34　kJ/mol)　for　the　H2CO*　hydrogenation　is　more　than　the　desorption　energy　of　54.80　kJ/mol,　H2CO　gas　was　the　main　product　from　the　hydrogenation　of　CO2　and　CO　on　a　pure　Cu(100)　surface.　For　the　Co-4/Cu(100)　surface,　the　optimal　pathways　for　the　CO2　and　CO　methanation　were　the　same　as　those　on　the　Cu(100)　surface.　The　rate-limiting　step　for　CO2　and　CO　methanation　is　the　H2COO*　(barrier　of　103.57　kJ/mol)　and　H2CO*　hydrogenation　(barrier　of　107.80　kJ/mol).　Compared　to　the　mechanism　of　CO2　and　CO　over　Cu(100),　the　Co　dopant　can　modify　the　rate-limiting　step　and　decrease　the　activation　barrier.　Particularly,　the　barrier　for　the　H2COH　decomposition　was　changed　from　100.96　kJ/mol　to　69.81　kJ/mol　(CO2　pathway)　and　61.26　kJ/mol　(CO　pathway).　Furthermore,　the　co-adsorbed　OH*　group　affects　the　hydrogenation　pathway　of　some　intermediates　rather　than　electronic　structures.