Human immunodeficiency virus type 1 integrase (IN) is an essential enzyme in the life cycle of this virus and also an important target for the study of anti-HIV drugs. In this work, the binding modes of the wild type IN core domain and the two mutants, that is, W132G and C130S, with the 4-hydroxycoumarin compound NSC158393 were evaluated by using the "relaxed complex" molecular docking approach combined with molecular dynamics (MD) simulations. Based on the monomer MD simulations, both of the two substitutions affect not only the stability of the 128-136 peptides, but also the flexibility of the functional 140s loop. In principle, NSC158393 binds the 128-136 peptides of IN; however, the specific binding modes for the three systems are various. According to the binding mode of NSC158393 with WT, NSC158393 can effectively interfere with the stability of the IN dimer by causing a steric hindrance around the monomer interface. Additionally, through the comparative analysis of the MD trajectories of the wild type IN and the IN-NSC158393 complex, we found that NSC15893 may also exert its inhibitory function by diminishing the mobility of the function loop of IN. Three key binding residues, that is, W131, K136, and G134, were discovered by energy decomposition calculated with the Molecular Mechanics Generalized Born Surface Area method. Characterized by the largest binding affinity, W131 is likely to be indispensable for the ligand binding. All the above results are consistent with experiment data, providing us some helpful information for understanding the mechanism of the coumarin-based inhibitors.