The rigorous coupled-wave analysis is used to describe the diffraction of multi-layer diffraction grating (MDG) with trapezium groove. The diffraction performance of multi-layer dielectric grating with the trapezium groove of 70° is discussed. Trapezium MDG used for wavelength of 1053 nm and incident angle of 51.2° is designed by optimizing the duty cycle, depth and residual thickness of the top layer. For gratings etched into the top HfO2 layer, diffraction efficiency of 99.5% can be attained when the duty cycle is 0.35, groove depth is 200 nm and the residual thickness of HfO2 is 50nm. Whereas for SiO2 as the top corrugated layer, the groove depth is 800 nm and the top SiO2 residual layer is 320 nm in order to obtain the same diffraction efficiency as 99.5%. Furthermore, the trapezium MDG with HfO2 on the top has wider wavebandth compared with the design of SiO2 on the top of MDG to obtain the same diffraction efficiency. Numerical calculation indicates that the coupled-wave analysis model has excellent convergence and stable performance to analyze the diffraction of trapezium MDG.