Transparent zinc oxide (ZnO) films on flexible copper-coated polyethylene terephthalate (PET) sheet have been grown by a potentiostatic cathodic deposition technique using aqueous zinc nitrate as electrolyte. ZnO films were fabricated using different deposition parameters such as applied potential, electrolyte concentration and bath temperature. Their structural and optical properties were characterized by X-ray diffractometer, scanning electron microscope, diffuse reflectance UV-VIS spectrophotometer and photoluminescence spectrometer. The effects of these deposition parameters on the structural and optical properties of the fabricated ZnO films have been investigated. On the basis of our results, we demonstrate that high quality ZnO films have been successfully grown on flexible polymeric substrates using a low temperature potentiostatic cathodic deposition technique.