In this study, the interaction between the coumarin derivative: N-(diphenylmethyl)-2-[(2-oxo-2H-chromen-4-yl)oxy]acetamide, biologically active drug, and human serum albumin (HSA) was investigated by using various optical spectroscopy techniques along with the computational technique. The results of steady-state fluorescence spectroscopy show that the static quenching occurred while increasing the coumarin drug concentration into HSA. Also, the binding constant (K) and thermodynamical parameters of enthalpy change (ΔH°), entropy change (ΔS°), and Gibbs free energy change (ΔG°) were calculated at different temperatures (293 K, 298 K, and 303 K). The results are in good agreement with those of molecular docking studies, and also, the docking study was carried out to understand the hydrogen bonding and hydrophobic interaction between human serum albumin and coumarin derivative. In addition to the docking, charge distribution analysis was done to understand the internal stability of coumarin derivative active sites of human serum albumin. Further time-resolved emission spectroscopy (TRES) studies were carried out between free HSA and HSA-coumarin complex, and the result confirms the presence of the drug in the protein molecule without cytotoxicity.