Vertically aligned ZnO nanorods were synthesized on a polyethylene naphthalate (PEN) substrate using a chemical bath deposition method at a low temperature. The structural and optical investigations revealed the high quality of the fabricated ZnO nanorods on flexible substrate. A metal-semiconductor-metal UV photodetector based on ZnO nanorods was fabricated on the PEN substrate. The optoelectronic characteristics of fabricated UV photodetector were studied in the dark and under 325 nm UV light illumination at −3 V and 3 V bias voltages. The responsivity and photosensitivity of the ZnO nanorod UV photodetector were 2.856 A/W and 1175% at 3 V bias voltage, respectively. Moreover, the response and the recovery times measured during the turn-on and turnoff of UV illumination were 1.2 s and 1.8 s, respectively.