The cholesteric liquid crystal can be regarded as a multilayer which consists of many layer uniaxial thin films which exhibit optical rotation. For the convenient discussion of the optical properties of cholesteric liquid crystal a new 2×2 matrix is offered, whose matrix element is the complex exponential. We discuss this method in detail and the role of it in the investigation of the optical property of the cholesteric liquid crystal. It is concluded that if the wavelength of incident light is equal to pitch of the cholesteric liquid crystal, the linear polarized light is changed into the circular polarized light. We also study the mechanism of the selective reflection of cholesteric liquid crystal for visible light when light propagates along the cholesteric liquid crystal.