In this study, metal-semiconductor-metal (MSM) ultraviolet (UV) photodetectors (PDs) based on Cu-doped ZnO (CZO) nanorods (NRs) were fabricated and investigated. The CZO NRs were prepared on a Corning glass substrate by the chemical bath deposition (CBD) method with photolithography processes. It was found that the diameter and length of ZnO NRs increased with Cu-doped concentration. The X-ray diffraction (XRD) analysis showed that the growth of NR arrays along the c-axis was hexagonal wurtzite crystal. Compared with pure ZnO NRs, it can be seen that the main UV peak (378 nm) of photoluminescence (PL) spectra showed a blue-shift phenomenon with the increase of Cu-doped concentration. Additionally, it was found that the rise and recovery time of such a fabricated PD were shortened under the UV illumination. The UV sensing properties of the CZO PDs were improved since the trapping and de-trapping of electrons by Cu-related complexes were faster than the adsorption and desorption of oxygen molecules. With a 3 V applied bias and 380 nm UV illumination, the optimal sensitivity of our PDs is 196.6.