We use a phenomenological nucleus-nucleus optical potential constructed in the light of a potential developed by Ginocchio[1] to study the elastic angular distributions of different nuclear systems near Coulomb barrier. The differential cross section ratios of elastic to Rutherford are studied for systems 14 N+ 56 Fe and 14 N+ 90 Zr for several colliding energies. Our theoretical predictions are well competitive with the experimental data, and the significantly small imaginary part of the potential explains the elastic scattering cross section and threshold anomaly in both systems.