Complex modulating properties of a twisted-nemetic liquid crystal spatial light modulator (TNLCSLM) are analyzed and simulated based on theories of the Jones matrix and the elastic free energy. As a further example,the first-order diffraction efficiency of a grating pattern displayed on the TN-LCSLM is calculated. It is found that there exists a maximum of the first-order diffraction efficiency even when the output polarizer is placed or not.