Based on the expression of phase delay and the expression of diffraction efficiency of diffractive optical elements (DOEs), the expression of diffraction efficiency of multilayer diffractive optical elements (MLDOEs) is described. The mathematical analysis model of diffraction efficiency for MLDOEs with decenter error is presented, and effects of decenter error on diffraction efficiency and polychromatic integral diffraction efficiency of MLDOEs are analyzed in long infrared waveband of 8~12 μm . ZnS and Ge are selected as the material of first and second harmonic diffractive optical elements respectively for the MLDOEs, the design wavelengths λ1 and λ2 are determined with 8.79 μm and 11.11 μm . The micro- structure height of MLDOEs are 78.3391 μm and 34.6076 μm , respectively. Finally, with the period width of MLDOEs 500 μm and 1000 μm , the range values of decenter error must be smaller than 5.8 μm and 11.71 μm when polychromatic integral diffraction efficiency is greater than 95% . The analysis model of diffraction efficiency with decenter error is important to manufacture and design process of MLDOEs.