Naproxen (N) is a member of nonsteroidal anti-inflammation drug and widely used as an analgesic, antipyretic, and anti-inflammation agent. In this investigation, the inherent stability and biochemical interaction of Naproxen and its related molecules have been studied. Density functional theory (DFT) with B3LYP/ 6-31G (d, p) has been employed to optimize the structures. Frontier molecular orbital features (HOMO-LUMO gap, hardness, softness), dipole moment, electrostatic potential and thermodynamic properties (electronic energy, enthalpy, Gibb’s free energy) of these optimized drugs are investigated. Molecular docking has been performed against prostaglandin H2 (PGH2) synthase protein 5F19 to search the binding affinity and mode(s) of all compounds. It is found that, all compounds are thermodynamically stable; some of them are chemically more reactive and show better binding affinity than the parent drug. ADMET calculations predict the improved pharmacokinetic properties of all compounds. Finally, this study can be helpful for the design of new analgesic, antipyretic drug.