This work presents a new procedure to determine the electrophoretic motion of a solid and insulating particle. P freely suspended in a viscous electrolyte in proximity of a plane boundary Sigma. The applied electric field E-infinity is uniform and either parallel or normal to the plane wall. The advocated approach applies to the general case of a particle of arbitrarily smooth shape and zeta potential Our method actually rests on the treatment of seven Fredholm boundary integral equations on the particle's surface and circumvents the computation of the electric field and the electrolyte flow in the whole fluid domain.