The conductivity of a concentrated suspension of charged spherical particles at an arbitrary level of surface potential is estimated. The cell model proposed by Kuwabara is adopted to simulate the present many-body problem by taking the effect of double-layer polarization into account. Several interesting results are found which cannot be observed if the corresponding linearized model is considered. For example, if phi (r) has a medium value? (K*/K-infinity) has a local minimum as kappaa varies, phi (r), K*, K infinity, kappa, and a being respectively the scaled surface potential, the effective conductivity, the effective conductivity for an infinitely dilute dispersion, the reciprocal Debye length, and the radius of a particle. For both kappa alpha -> 0 and kappa alpha -> infinity, (K*/K-infinity) decreases with the increase in the volume fraction of the dispersed phase, and the reverse is true for a medium Ka. For a fixed kappa alpha, the variation of (K*/K-infinity) as a function of phi (r) may have a local minimum as alpha (=valence of counterions/valence of co-ions) varies. For a fixed phi (r), the variation of (K*/K-infinity) as a function of kappa alpha may have a local minimum as alpha varies.