The present research investigates the application of the green method to produce nanocomposites. The CuO/PET fiber nanocomposite can be prepared in two ways. The first way involves the application of the electrospinning technique by which waste plastic cups of polyethylene terephthalate (PET) are converted into nanofibers. In the second way, the copper nanoparticle (CuONPs) is synthesized with the natural capped plant extract of sumac (Rhus Coriaria L., family Anacardiaceae) and the CuONPs are then combined as a filler with the PET nanofiber using a cross-linked solvent. The X-ray diffraction (XRD), transmission electron microscopy (TEM), field emission scanning electron microscopy (FESEM), energy dispersion spectroscopy (EDS), and map elements distribution can be applied to investigate the surface modification and alteration of the composite nanofiber morphology. The collected data show that the produced CuO/PET nanocomposites have a high surface area, well distribution of elements, magnificent shape, and stable dispersion state. Furthermore, the CuO/PET nanocomposites are considered as an efficient photocatalytic removal of the toxic methylene blue dye (MB) in aqueous solutions. The results of the present study demonstrate that the photocatalytic efficiency for removing MB dye is achieved in a short time using a low-intensity irradiation ultraviolet light.