The electrocatalytic CO2 reduction reaction (CO2RR) represents an effective way to address energy crises and environmental issues by converting CO2 into valuable chemicals. Single-atom catalysts (SACs) can achieve excellent catalytic activity in CO2RR. However, the study of CO2RR on SACs still poses significant challenges, especially in terms of controlling the selectivity towards the deep product such as CH4 and CH3OH. Herein, we employ density functional theory (DFT) calculations to investigate the CO2RR on the Cu single-atom catalysts supported on N-doped graphene (Cu-N/C) and explore the role of N dopants on the CO2RR performance. The results predict that, compared to Cu SACs supported on N-doped defective graphene with double vacancy (Cu-N/C-DV), Cu SACs supported on N-doped defective graphene with single vacancy (Cu-N/C-SV) can effectively convert CO2 into the deeply reduced C1 products, including CH4 and CH3OH. The results further indicate that Cu-N/C-SV has a stronger interaction with *CO, which is conducive to the deep reduction of *CO. Increasing the coordination number of N atoms or the proximity of the doping site to Cu active site can effectively enhance the stability of the catalyst and promote the adsorption of *CO on Cu-N/C-SV. However, this also increases the free energy of the formation of *CHO intermediate. The results indicate that CuC3-Nm, which contains an N atom in the second coordination shell (meta-position) of Cu SACs, has the best electrocatalytic performance of CO2RR in terms of both selectivity and catalytic activity. These results not only contribute to an in-depth understanding of the reaction mechanism of CO2RR on SACs but also provide insights into the design of SACs for efficient CO2RR.