To create a sensitive photodetector, the transparent and conductive properties of graphene and the optical and photovoltaic properties of poly(3-hexylthiophene) (P3HT) are combined as a hybrid composite. Based on the inherent nature of the band alignment between graphene and P3HT, the photogenerated holes are able to transfer to the graphene layer and improve the photoresponse to be much better than the traditional layer by layer organic system. Additionally, the graphene is deposited on a piezoelectric Pb(Zr0.2Ti0.8)O-3 (PZT) substrate, and the photoresponse of such composite photodetectors is found to be ten times larger than on SiO2 base. It is demonstrated that the electric field of the polarization of piezoelectric substrate helps the spatial separation of photogenerated electrons and holes and promotes the hole doping of graphene to enhance the photoconduction. A detailed investigation of graphene layers, thickness of P3HT and time evolution shows that the composite of graphene and P3HT on PZT can be used as a sensitive photodetector and has potential as an effective solar cell. Moreover, with the replacement of P3HT by a thin layer of bulk heterojunction of polymer and fullerene, the photosensitivity can be further increased by more than one order of magnitude.