The emergence of coronavirus disease 2019 (COVID-19) pandemic caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has been bringing the world to a standstill. Beyond all doubt, the most striking therapeutic target for antibody development is the spike (S) protein on the surface of virus. In contrast with an immunodominant receptor-binding domain (RBD) of the spike protein, little is known about neutralizing antibodies binding mechanisms of N-terminal domain (NTD), let alone the effect of NTD mutation on antibody binding and risk of immune evasion. Employing various computational approaches in this study, we investigated critical residues for NTD-antibody bindings and their detailed mechanism. The results showed that some residues on NTD including Y144, K147, R246 and Y248 are critically involved in the direct interaction of NTD with many monoclonal antibodies (mAbs), indicating that the viruses harboring these residue mutations may have high risk of immune evasion. Binding free energy calculations and the interaction mechanism study revealed that R246I, which is present in Beta (B.1.351) variant, may decrease or even abrogate the efficacies of many antibodies. Therefore, special attention should be paid to the mutations of the 4 residues for future antibody design and development.