A first dielectric wall and a second dielectric wall in which hollow alumina cylindrical columns are arranged in layers so that axial centers of the alumina cylindrical columns describe planar triangular lattice arrays, are opposed to each other, and are parallel to air interposed between them. Metal plates are opposed to each other and have end faces of the alumina cylindrical columns interposed between and connected to the metal plates. The first and second dielectric walls and the metal plates are bonded to one another, as a high-frequency waveguide with reduced radiation loss, and that is inexpensive and low in transmission loss.