The approximate solutions of Schrodinger equation for the Hua plus modified Eckart (HPME) potential is obtained via the Formula method. The vibrational partition function and other thermodynamic properties were investigated. Using the Hellmann-Feynman theorem, the expectation values of r -2, T and p2 and their numerical values are also presented. Some cases of this potential are also studied. The results of our study are consistent with those in literature.