The Poisson-Boltzmann equation has been solved to obtain the electrostatic potential for the spherical cell model of a fullerene molecule at which charged groups are attached. The electrostatic internal and free energies, degree of binding of counterions, osmotic coefficient, and distribution of counterions around the charged fullerene shell are calculated. These properties are presented as functions of the concentration, radii of counterions, and surface charge density of the fullerene macroion. Calculated osmotic coefficients are compared with preliminary experimental data for the sodium salt of fullerenehexamalonic acid, C-66(COONa)(12).