The generalize Born (GB) model is frequently used in MD simulations of biomolecular systems in aqueous solution. The GB model is usually based on the so-called Coulomb field approximation (CFA) for the energy density integration. In this study, we report that the GB model with CFA overdestabilizes the long-range electrostatic attraction between oppositely charged molecules (ionic bond forming two-helix system and kinesin-tubulin system) when the energy density integration cutoff, r(max), which is used to calculate the Born energy, is set to a large value. We show that employing large r(max), which is usually expected to make simulation results more accurate, worsens the accuracy so that the attraction is changed into repulsion. It is demonstrated that the overdestabilization is caused by the overestimation of the desolvation penalty upon binding that originates from CFA. We point out that the overdestabilization can be corrected by employing a relatively small cutoff (r(max) = 10-15 angstrom), affirming that the GB models, even with CFA, can be used as a powerful tool to theoretically study the protein-protein interaction, particularly on its dynamical aspect, such as binding and unbinding.