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 Cu SAC supported on N-doped graphene (Cu-N/C) and explore the role of N dopants on the CO₂RR performance. Compared to Cu SACs sup ported 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, thus further indicating 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 doping site to the Cu active site can effectively enhance the stability of 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 suggest that CuC₃-N_m, which contains a 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, not only contributing to an in-depth understanding of the reaction mechanism of CO₂RR on SACs but also providing insights into the design of SACs for efficient CO₂RR.