Graphene-based photodetectors have attracted attention for realizing optoelectronic devices including photodetectors. We report a graphene field effect transistor on silicon for broadband light detection from the ultraviolet to near-infrared region, which is compatible with the silicon technology and does not need a complicated fabrication process. The photodetectors show an improved responsivity. Specifically, fabricated graphene photodetectors shows a photo-responsivity of ~980 A/W at room temperature. These results provide a promising for the development of graphene-based optoelectronic applications with the broadband photodetection from the ultraviolet to near-infrared region.