Thermodynamic properties of five diatomic molecules such as H2, HF, I2, N2 and O2 have been theoretically predicted. To this end, the interaction potential of the diatomic molecules has been considered as the Tietz–Hua (TH) potential model. Then, the Schrodinger equation was solved for the potential and energy eigenvalues were obtained in the closed form by using the Nikiforov–Uvanov (NU) method. Using the energy eigenvalues, we have determined partition function, mean energy, specific heat at constant pressure and volume, entropy and enthalpy of the diatomic molecules and compared with experimental data. Our results were in good agreement with experimental data. It is found that the Tietz–Hua potential model is a suitable case to predict thermodynamic functions of H2, HF, I2, N2 and O2 molecules at wide ranges of temperatures.