According to the theory of phase retardation expression, the relation between the phase retardation function of multi-layer diffractive optical element (MLDOE) with Cauchy dispersion approximate refractive indices formula and characteristics of material, along with the relation between diffraction efficiency and design wavelengths are studied. In the visible region from 400 to 700 nm, the MLDOE consists of two harmonic diffractive elements with different dispersive optical materials such as polymethyl methacrylate and polycarbonate. The maximum bandwidth integrated average diffraction efficiency (BIADE) of the MLDOE designed with Cauchy dispersion approximate refractive indices formula is 99.62%, and the corresponding design wavelengths are 440.5 nm and 605.5 nm. The diffraction efficiency of BIADE and of MLDOE is analyzed with design wavelengths of thispaper and other methods. Distribution error of diffraction efficiencies is given, which proves that the diffraction efficiencies of MLDOE are independent on materials but dependent on design wavelengths only.