Optical characteristics of a Fabry-Perot interferometer using cholesteric liquid crystal (CLC) are analyzed rigorously based on electro-magnetic wave equations. Being different from the conventional Fabry-Perot interferometer, the minimum cavity length for resonance is a quarter of wavelength, not half of wavelength. When the refractive indices of the CLC mirrors and Material inside the cavity are the same, perfect circular polarization resonance with high finesse is obtained for the incident circularly polarized light.