A photonic band-gap optical fiber is disclosed. The photonic band-gap optical fiber includes a photonic crystal having plural band-gaps. The photonic crystal includes a first medium having a first permittivity; plural second media having a second permittivity, and formed in a first periodic arrangement with respect to at least one or more directions on a plane formed of the first medium; and plural third media having a third permittivity, formed in a second periodic arrangement with respect to at least one or more directions on the plane formed of the first medium, and formed in a third periodic arrangement with respect to at least one or more directions together with the plural second media. The photonic crystal has a hollow portion for propagating light passing through the plane formed of the first medium. The photonic band-gap optical fiber can be used to propagate light of plural, different bands at the same time.