Depression, a mental disorder that plagues the world, is a burden on many families. There is a great need for new, fast-acting antidepressants to be developed. N-methyl-D-aspartic acid (NMDA) is an ionotropic glutamate receptor that plays an important role in learning and memory processes and its TMD region is considered as a potential target to treat depression. However, due to the unclear binding sites and pathways, the mechanism of drug binding lacks basic explanation, which brings great complexity to the development of new drugs. In this study, we investigated the binding affinity and mechanisms of an FDA-approved antidepressant (S-ketamine) and seven potential antidepressants (R-ketamine, memantine, lanicemine, dextromethorphan, Ro 25-6981, ifenprodil, and traxoprodil) targeting the NMDA receptor by ligand–protein docking and molecular dynamics simulations. The results indicated that Ro 25-6981 has the strongest binding affinity to the TMD region of the NMDA receptor among the eight selected drugs, suggesting its potential effective inhibitory effect. We also calculated the critical binding-site residues at the active site and found that residues Leu124 and Met63 contributed the most to the binding energy by decomposing the free energy contributions on a per-residue basis. We further compared S-ketamine and its chiral molecule, R-ketamine, and found that R-ketamine had a stronger binding capacity to the NMDA receptor. This study provides a computational reference for the treatment of depression targeting NMDA receptors, and the proposed results will provide potential strategies for further antidepressant development and is a useful resource for the future discovery of fast-acting antidepressant candidates.