The electrophoretic behavior of a sphere in a spherical cavity is examined theoretically. We show that if the applied electric field is low, the mobility exhibits a local minimum as the thickness of double layer varies. This local minimum disappears if the applied electric field is high. If double layer is thin, the mobility becomes independent of the surface potential of the particle and the applied electric field. For low surface potentials, the mobility decreases with the increase in the applied electric field, but the reverse in true if the surface potential is high. If an electric field is applied in the direction from the bottom of the particle to its top, counterions are concentrated on the bottom of the particle. The presence of cavity wall will affect the thickness of double layer and the degree of double-layer polarization. For the case of thick double layer and small (particle radius/cavity radius) ratio, the contours of net space charge density near the cavity wall become elliptical.