Molecular simulations rely heavily on a long range electrostatic Coulomb interaction. The Coulomb potential decays inversely with distance, indicating infinite effective range. In practice, molecular simulations do not directly take into account such an infinite interaction. Therefore, the Ewald, fast multipole, and cutoff methods are frequently used. Although cutoff methods are implemented easily and the calculations are fast, it has been pointed out that they produce serious artifacts. Wolf and coworkers recently discovered one source of the artifacts. They found that when the total charge in a cutoff sphere disappeared, the cutoff error is dramatically suppressed. The Wolf method uses the charge-neutral principle combined with a potential damping that is realized using a complementary error function. To date, many molecular simulation studies have demonstrated the accuracy and reliability of the Wolf method. We propose a novel long-range potential that is constructed only from the charge-neutral condition of the Wolf method without potential damping. We also show that three simulation systems, in which involve liquid sodium-chloride, TIP3P water, and a charged protein in explicit waters with neutralized ions using the new potential, provide accurate statistical and dielectric properties when compared with the particle mesh Ewald method.