Working within the framework of the Coulomb modified Glauber model and the optical limit approximation, we propose a phenomenological method of analysis for heavy-ion elastic scattering data at intermediate energies. Instead of using the commonly employed Gaussian approximation for the input NN amplitude that is deficient in some respects at low intermediate energies, we evaluate it in terms of a three parameter phenomenological NN phase shift function. The application of the method to some 12 C -nucleus and 16 O -nucleus systems shows that a very good description of the elastic scattering data at several energies can be obtained in this way. In particular, the 12 C –12 C elastic scattering data at 200 MeV/nucleon is very well reproduced. We also calculate the effective NN potential using the phenomenological NN phase shift function by the method of inversion. The calculated potential shows the expected behavior and is found to vary smoothly with energy.