By extending an approximate theory of the electrophoretic mobility of dilute spherical colloidal particles in a salt-free medium containing only counterions (H. Ohshima, J. Colloid Interface Sci. 248 (2002) 499-503), a systematic numerical method is given for the calculation of the electrophoretic mobility, which is based on an iteration method. We assume that each sphere is surrounded by a spherical free volume, within which counterions are distributed so that electroneutrality is satisfied. The electrophoretic mobility is found to be determined mainly by the pressure due to the counterions at the outer surface of the free volume. It is shown how the mobility values deviate from those expected from Huckel's formula for high particle charges or zeta potentials because of the counterion condensation effect. (C) 2003 Elsevier Science (USA). All rights reserved.