ZnO/CuO nanofibers, with different CuO concentrations, were fabricated by one-step electrospinning of the polymer precursor and annealing in air. Scanning electron microscopy (SEM) showed smooth and beadless morphology for the synthesized nanofibers, while X-ray diffraction (XRD) analysis revealed formation of hexagonal and monoclinic crystalline structure phases for ZnO and CuO nanofibers, respectively. X-ray photoelectron spectroscopy (XPS) analysis confirmed the presence of CuO on the surface of ZnO nanofibers. For further confirming the formation of chemical bonds, Fourier transform infrared (FT-IR) spectroscopy was employed. The effect of Cu contents in the overall electronic band structure of ZnO was explained by density functional theory (DFT) calculations. Diffuse reflectance spectroscopy (DRS) showed that the ZnO band gap energy reduced with increasing amount of CuO contents due to the presence of the Cu(3d) energy states above the valence band. Comparing the photocatalytic activity of ZnO/CuO nanofiber samples with different CuO concentrations under similar sunlight irradiation conditions revealed that the ZnO/(0.5 wt %) CuO sample exhibited the highest performance among all samples. This was explained by an effective suppression of electron–hole recombination as verified by both photoluminescence (PL) and photocurrent density measurements. By means of charge carrier scavengers, it was found that holes and hydroxyl radicals are the main surface species for photocatalytic degradation of methylene blue (MB) over the ZnO/(0.5 wt %) CuO nanofiber. Furthermore, the optimized sample demonstrated great activity for the degradation of bisphenol A (BPA) with a rate constant of 3.4 × 10–2 min–1. Finally, a photocatalytic degradation mechanism based on the main reactive oxygen species (ROS) and calculated band positions was proposed.