Based on density functional theory (DFT), a two-dimensional(2D) metal-organic framework (MOF) based on Co and Cu atoms were presented. Based on the phonon dispersion calculations, no imaginary mode is found in the phonon branches, which verifies that the crystal structures of MOF could be stable. Based on the calculation of electronic band structure, it is found that the Cu-based MOF is a metallic system by applying external electric field. While the Co-based MOF undergoes a transition from metal to semiconductor under external electric field. When the external electric field intensity reaches up to 0.5 eV/Å, the band gap of Co-based MOF is around 0.1 eV, while this does not happen in the Cu-based MOF. Furthermore, the N₂ adsorption and the nitrogen reduction reaction (NRR) were investigated for the Co-based MOF, which shows that the NRR for the Co-based MOF exhibits good performance, and the electric field could enhance this effect of NRR. The free energy of NRR under external electric field of 0.5 eV/Å is 0.51 eV lower than that without electric field. Therefore, our study would prospectively guide the experimental researchers on the design of NRR.