We demonstrate switching of ionic conductivities in wedge-shaped liquid-crystalline (LC) ammonium salts. A thermoreversible phase transition between the rectangular columnar (Colr) and hexagonal columnar (Colh) phases is used for the switch. The ionic conductivities in the Colh phase are about four orders of magnitude higher than those in the Colr phase. The switching behavior of conductivity can be ascribed to the structural change of assembled ionic channels. X-ray experiments reveal a highly ordered packing of the ions in the Colr phase, which prevents the ion transport.