The grating used for chirped pulse compressor should have broad waveband and high diffraction efficiency. A metal-multilayer-dielectric grating (MMDG) with broad waveband and high diffraction efficiency is proposed to stretch and compress chirped pulse. It consists of three parts as substrate, metal and multi-layer dielectric mirror and surface relief structure. Rigorous coupled-wave analysis is employed to analyze the diffraction property of MMDG to extend working waveband and improve the diffraction efficiency. Simulation results show that when the groove depth, residual thickness, duty cycle and incident angle are 272 nm, 10 nm, 0.23 and 54° respectively, the average diffraction efficiency is higher than 97% for TE polarized light over the 150 nm bandwidth centered at 800 nm as the wavelength changes from 732 to 886 nm.