C2N monolayer has been proved to catalyze some important reaction, such as CO oxidation and N-2 reduction reaction efficiently due to the periodic porous structure and the electron enrichment on nitrogen atoms. However the catalytic performance of C2N in CO2 reduction still needs comprehensive investigation. In this work, the potential of Cu atom embedded C2N monolayer (Cu/C2N), as a single-atom catalyst (SACs) for hydrogenation of CO2 to formic acid, has been evaluated by the first-principles calculations. The computational results show that the reaction can proceed via two feasible mechanisms, named as path I and path II, which start from the initial co-adsorption of H-2 and CO2 on Cu/C2N (H-2 + CO2@Cu/C2N) and H-2 adsorption on Cu/C2N (H-2@Cu/C2N), respectively. Path II exhibits the obvious superiority due to the low barrier all through the whole channel. The highest energy barrier in path II is only 0.53 eV, which means that CO2 hydrogenation to formic could be realized on the Cu/C2N at the room temperature. The high activity of the single atom catalyst Cu/C2N implies the potential application in the industrial CO2 hydrogenation. This study also promotes a new path to design catalysts for the reduction of CO2 and further broadens the range of applications for C2N-based materials.