A waveguide based on a three-dimensional photonic crystal is arranged to provide wave-guiding in a single mode and a mode having a field strength distribution with unimodality in a plane perpendicular to the wave-guiding direction, to thereby enable wave-guiding in a desired frequency band, wherein the three-dimensional photonic crystal has a plurality of line defect members which include a first line defect member made of a medium having a refractive index not smaller than that of the columnar structures and formed in a direction perpendicular to the direction in which the columnar structures extend, and a second line defect member formed in the same direction as the first line defect member.