  In this study, we obtain the approximate analytical solutions of the radial
Schr\"{o}dinger equation for the Deng-Fan diatomic molecular potential by using
exact quantization rule approach. The wave functions have been expressed by
hypergeometric functions via the functional analysis approach. An extension to
rotational-vibrational energy eigenvalues of some diatomic molecules are also
presented. It is shown that the calculated energy levels are in good agreement
with the ones obtained previously $E_{n\ell}-D$ (shifted Deng-Fan).
