Electrochemical CO2 reduction reaction (CO2RR) to fuels represents one of the most attractive approaches to mitigate our pressing energy and environmental threats. Cu is the best known metal catalyst that can produce an appreciable amount of hydrocarbons from CO2, but it suffers from a high overpotential and poor selectivity. In this work, by means of first-principles calculations, we predict that Cu-based single-atom alloys (SAAs) could be exceptional electrocatalysts for CO2RR. In particular, we predict that Co@Cu SAA could be a promising catalyst on which methanol can be produced at a low overpotential and high selectivity. The isolated Co atoms lead to a narrowed d-band and an upshifted d-band center which can stabilize chemisorbed CO2 on a surface, significantly lowering the reaction barrier. The narrowed Co d-band increases the bonding to a key intermediate, which in turn eliminates the need for its migration and enables a selective and efficient production of CH3OH through the pathway of CO2 → COOH* → CO* → COH* → CHOH* → CH2OH* → CH3OH.