Graphene/semiconductor Schottky junctions are an emerging field for high-performance optoelectronic devices. This study investigates not only the steady state but also the transient photoresponse of graphene field-effect transistor (G-FET) of which gate bias is applied through the Schottky barrier formed at an n-type Si/graphene interface with a thin oxide layer, where the oxide thickness is sufficiently thin for tunneling of the charge carrier. To analyze the photoresponse, we formulate the charge accumulation process at the n-Si/graphene interface, where the tunneling process through the SiOx layer to graphene occurs along with recombination of the accumulated holes and the electrons in the graphene at the surface states on the SiOx layer. Numerical calculations show good qualitative agreement with the experimentally obtained results for the photoresponse of G-FET.