As a developing technology for flexible electronic device fabrication, ultra-violet (UV) photodetectors (PDs) based on a ZnO nanostructure are an effective approach for large-area integration of sensors on nonconventional substrates, such as plastic or paper. However, photoconductive ZnO nanorods grown on flexible substrates have slow responses or recovery as well as low spectral responsivity R because of the native defects and inferior crystallinity of hydrothermally grown ZnO nanorods at low temperatures. In this study, ZnO nanorod crystallites are doped with Cu or Ni/Cu when grown on polyethylene terephthalate (PET) substrates in an attempt to improve the performance of flexible PDs. The doping with Ni/Cu or Cu not only improves the crystalline quality but also significantly suppresses the density of deep-level emission defects in as-grown ZnO nanorods, as demonstrated by X-ray diffraction and photoluminescence. Furthermore, the X-ray photoelectron spectroscopy analysis shows that doping with the transition metals significantly increases the oxygen bonding with metal ions with enhanced O/Zn stoichiometry in as-grown nanorods. The fabricated flexible PD devices based on an interdigitated electrode structure demonstrates a very high R of ~123 A/W, a high on-off current ratio of ~130, and a significant improvement in transient response speed exhibiting rise and fall time of ~8 and ~3 s, respectively, by using the ZnO nanorods codoped by Ni/Cu.