A perturbation solution based on the curvature of the surface of a particle is derived for the electrical potential of two planar, cylindrical, and spherical colloidal particles immersed in a salt-free medium. Compared with the available results in the literature, the present approach improves both the accuracy and the applicable range in the level of the surface potential, the valence of counterions, and the thickness of the double-layer surrounding a particle. The zero-order perturbation solution is exact for the case of two planar particles. Under typical conditions, the averaged percentage deviation of the first-order perturbation solution is on the order of ca. 5% for both two cylindrical and two spherical particles. (C) 2010 Elsevier Inc. All rights reserved.