To describe the diffusion of ions in a water-swollen membrane, we improved the Nernst-Planck equation of ion flux by considering a frictional force generated by the collision of ions with membrane matrix which depends on membrane potential. This new equation of ion flux predicts that the apparent mobility of an ion in a membrane depends on both the membrane potential and the valence of the ion. The experimental data of diffusion in dialysis systems of KCl, LiCl, CaCl2, and LaCl3 were consistent with the predictions based on this equation.