In this report, we present a photosensing unit based on single-walled nanotubes (SWNTs) integrated with Cu2O/ZnO hybrid nanofilms. 50-nm Cu2O and 50-nm ZnO nanofilms are respectively deposited on a SWNTs-coated polyethylene terephthalate (PET) sheet via a two-step sputtering process. The Cu2O/ZnO nanofilm photodetector exhibits rapid response (<100 ms), excellent responsive repeatability, robust stability and broadband photodetection range from 365 to 625 nm without external bias. Furthermore, ZnO/Cu2O nanofilm photodetector has been also fabricated by changing deposition sequence of ZnO and Cu2O. The photocurrent of the ZnO/Cu2O nanofilm photodetector is one-fourth of that of the Cu2O/ZnO nanofilm photodetector. We speculate that it might be attributed to the presence of the whispering-gallery mode (WGM) resonances in Cu2O/ZnO hybrid nanofilms owing to the higher refractive index of Cu2O, resulting in enhancing the light trapping and absorption. The high performance of Cu2O/ZnO nanofilm photodetector indicates that the Cu2O/ZnO hybrid nanofilms on SWNTs-based conducting substrates are suitable for mass production and application as high-sensitivity, fast response speed and flexible UV/visible photodetectors.