We investigate the mechanism of light extraction enhancement of a GaN-based light-emitting diode (LED) grown on patterned sapphire substrate (PSS), that has ZnO nanorod arrays (NRAs) fabricated on top of the device using the hydrothermal method. We found that the light output power of the LED with ZnO NRAs increases by approximately 30% compared to the conventional LED without damaging the electrical properties of the device. We argue that the gradual decrease of the effective refractive index, which is caused by the fabrication of ZnO NRAs, is the mechanism of the observed improvement. Our argument is confirmed by cross-sectional confocal scanning electroluminescence microscopy (CSEM) and the theoretical simulations, where we observed a distinct increase of the transmission at the interface between LED and air at the operation wavelength of the LED. In addition, the plane-view CSEM results indicate that ZnO NRAs, which were grown on the bare p-type GaN layer as an electrical safety margin area, also contribute to the enhanced light output power of the LED, which indicate further enhancement is manifested even in the optically ineffective sacrificial area.