An analysis of the electrophoretic motion of charged colloidal particles in a concentrated suspension is developed to predict the electrophoretic mobility of the particles and the electrical conductivity of the suspension. The analysis is based on a unit cell model that takes into account particle-particle hydrodynamic interactions and includes relatively thick electric double layers. The fluid motion in the unit cell is treated by writing the relevant Navier-Stokes equation in terms of the stream function and vorticity. The governing equations were then solved by a finite-difference method. The calculated electrophoretic mobilities are in agreement with prior analytical solutions for moderately concentrated suspensions, and the theory reduces to the result of O'Brien and White for low to moderate zeta potentials and dilute suspensions and to the classical result of Smoluchowski for thin double layers and dilute suspensions. A parametric study shows that the electrical conductivity of the suspension relative to a free electrolyte solution is affected by the counterion to co-ion diffusivity ratio, the double-layer thickness, and the volume fraction of particles. For a dispersion of moderately charged particles (moderate zeta potentials) with thick double layers, the numerical model predicts the electrical conductivity in agreement with experimental values reported in the literature.