An optical diode (OD) and its application based on the photonic band-gap (PBG) property of chiral photonic crystals are presented. The OD is constructed from wave-plates and cholesteric liquid crystals with two different pitches. The component is polarization sensitive and exhibits passive anisotropic transmission analogous to the electronic diode. The non-reciprocal transmission of linearly polarized light at the different PBG regions is discussed. A new scheme of a color-separating system with the OD is proposed. The OD behavior constitutes the operational mechanism for a color splitter.