The Deng-Fan-Eckart potential is as good as the Morse potential in studying atomic interaction in diatomic molecules. By using the improved Pekeris-type approximation, to deal with the centrifugal term, we obtain the bound-state solutions of the radial Schrodinger equation with this adopted molecular model via the Factorization Method. With the energy equation obtained, the thermodynamic properties of some selected diatomic molecules (H-2, CO, ScN and ScF) were obtained using Poisson summation method. The unnormalized wave function is also derived. The energy spectrum for a set of diatomic molecules for different values of the vibrational n and rotational l\ are obtained. To show the accuracy of our results, we discuss some special cases by adjusting some potential parameters and also compute the numerical eigenvalue of the Deng-Fan potential for comparison sake. However, it was found out that our results agree excellently with the results obtained via other methods.