In order to design a multilayer dielectric grating with wide-bandwidth diffraction spectrum, the restriction factors of both the reflection bandwidth of multilayer dielectric high-reflectivity mirror and the guided-mode resonance phenomenon are studied in detail. The reflection characteristics of high-reflectivity mirror in zeroth and — 1st transmitted diffraction orders are quantitatively evaluated. It is found that the reflection bandwidth of high-reflectivity mirror in — 1st transmitted diffraction order, which determines the final diffraction bandwidth of multilayer dielectric grating, is evidently compressed. Furthermore, it is demonstrated that the reducing of grating period is an effective approach to the elimination of guided mode resonance over a required broad band range both spectrally and angularly. In addition, the expressions for calculating the maximum period ensuring no guided mode resonance in the required bandwidth are derived. Finally, two high-efficiency pulse-compression gratings with broad-band are presented.