An efficient and effective method to achieve high responsivity and specific detectivity, particularly for normal-incident quantum well infrared photodetectors (QWIPs), is proposed in this study. By combining superlattice (SL) structure, grating structures, and graphene monolayer onto traditional QWIP designs, a graphene-covered multicolor quantum grid infrared photodetector (QGIP) with improved optoelectrical properties is developed. The enhancements of the device's responsivity and specific detectivity are about 7-fold and 20-fold, respectively, which resulted from an increase in the charge depletion region and the generation of extra photoelectrons due to graphene-semiconductor heterojunction. This method provides a potential candidate for future high-performance photodetectors.