The rigorous coupled-wave analysis technique for describing the diffraction of metal multi-layer diffraction grating (MMDG) is built. Formulation for a stable and efficient numerical implementation of diffraction efficiency is presented for MMDG with TE polarization. With the merit function of the -1 order diffraction efficiency higher than 97% and working bandwidth, the parameters of MMDG are optimized to achieve broadband. The bandwidths used for 800 nm and 1053 nm can be 130 nm and 150 nm respectively. The manufacture latitude and the effective incident angle for the optimized structure of MMDG are discussed. The optimized grating should be useful for chirped pulse compress.