Poly(ethylene terephthalate) PET, track-etched membranes (TeMs) with 400 nm average pore size were UV grafted with poly(acrylic acid) (PAA) after oxidation of inner surfaces by H2O2/UV system. Carboxylate groups of grafted PAA chains were easily complexed with Cu2+ ions in aqueous solutions. These ions were converted into metallic copper nanoparticles (NPs) by radiation-induced reduction of copper ions in aqueous-alcohol solution by gamma rays in the dose range of 46-250 kGy. Copper ions chelating with-COOH groups of PAA chains grafted on PET TeMs form polymer-metal ion complex that prevent the formation of agglomerates during reduction of copper ions to metallic nanoparticles. The detailed analysis by X-Ray diffraction technique (XRD), transmission electron microscopy (TEM), scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDX) confirmed the deposition of copper nanoparticles with the average size of 70 nm on the inner surface of nanochannels of PET TeMs. Samples were also investigated by FTIR, ESR spectroscopies to follow copper ion reduction.