This paper reports the successful coating of carbon nanotubes (CNTs) grown on a metallic surface with particles of a ceramic dielectric material by using the electrophoretic deposition technique. Electrophoretic deposition, which is performed at room temperature, has achieved results that are far superior to chemical vapor deposition in this particular application. In an anticipated new breed of capacitors known as the "three-dimensional capacitors," conventional metallic electrodes will be replaced by CNTs for substantially larger electrode areas. The development of such capacitors is awaiting a technique for successfully coating CNTs with high dielectric-constant ceramics. Such a development is reported here.