Lightweight and flexible ultraviolet (UV) photodetectors (PDs) are of increasing interest for modern applications such as wearable devices, synthetic skins, and robotics. A strong, reliable response under low driving voltages and over a broad working range of incident light intensities is highly desired for such UV PDs. To date, most of the commercial UV PDs are based on photomultiplier tubes (PMTs) and gallium nitride p-n junction photodiodes. However, the fragile vacuum tube and the requirement of extremely high driving voltages make PMT-based UV PDs ill-suited for many applications out in the field. Inorganic photodiodes are rigid, necessitate thick active films, and require complex and expensive processing. In contrast, thin film UV PDs based on organic-inorganic nanocomposite have high sensitivity, adjustable response range, lightweight, mechanical flexibility, and solution processability, making them promising for wider applications. In this work, UV PDs based on F8T2:ZnO quantum dots (QDs) nanocomposite with different weight ratios were fabricated with the structure of ITO/PEDOT:PSS/F8T2:ZnO QDs/BCP/Al on PET substrates, where ITO serves as anode, PEDOT:PSS works as a hole transport layer, F8T2:ZnO QDs works as the active layer, BCP functions as an electron transport/hole blocking layer, and Al serves as cathode. Under dark and reverse bias, holes are blocked by BCP due to the large energy barrier of 2.8 eV between the work function of Al (-4.2 eV) and the HOMO of BCP (-7.0 eV) and electrons would be difficult to inject from ITO to the active layer due to the high energy barrier of 2.1 eV between the HOMO of PEDOT:PSS (-5.2 eV) and the LUMO of F8T2 (-3.1 eV) because more F8T2 are close to the PEDOT:PSS layer. Photomultiplication was achieved by control the distribution of ZnO QDs in the active layer. More ZnO QDs in the active layer close to the Al cathode can effectively trap electrons under UV illumination, leading to band bending, which allows hole injection from Al cathode into the active layer under reverse bias, and hole transfer through the active layer and collected by ITO anode. Devices with F8T2:ZnO weight ratio in the range of 1:10-1:3 showed a low dark current density in the low 10-6 mA/cm2 under -2 V reverse bias. A narrow EQE peak centered at 354 nm exhibited ~16000% under -3 V reverse bias with the full width at half maximum (FWHM) of 14 nm, which is due to the wavelength dependence of the light penetration depth in the active layer. Hole-only devices were fabricated to understand the device working mechanism. The devices were bended to a curvature radius of 0.7 cm for 150 times. The dark current, UV photocurrent, and photoresponse rate remained unchanged before and after bending while EQE dropped slightly. All the results demonstrated F8T2:ZnO as a promising candidate for making lightweight, flexible UV PDs with tunable photoresponse range.