Copper electrodes with a micromesh/nanomesh structure were fabricated on a polyimide substrate using UV lithography and wet etching to produce flexible transparent conducting electrodes (TCEs). Well-defined mesh electrodes were realized through the use of high-quality Cu thin films. The films were fabricated using radio-frequency (RF) sputtering with a single-crystal Cu target--a simple but innovative approach that overcame the low oxidation resistance of ordinary Cu. Hybrid Cu mesh electrodes were fabricated by adding a capping layer of either ZnO or Al-doped ZnO. The sheet resistance and the transmittance of the electrode with an Al-doped ZnO capping layer were 6.197 ohm/sq and 90.657%, respectively, and the figure of merit was 60.502 × 10(-3)/ohm, which remained relatively unchanged after thermal annealing at 200 °C and 1,000 cycles of bending. This fabrication technique enables the mass production of large-area flexible TCEs, and the stability and high performance of Cu mesh hybrid electrodes in harsh environments suggests they have strong potential for application in smart displays and solar cells.