The nano-imprint lithography method was employed to incorporate wide-area (375 x 330 mum(2)) photonic-crystal (PC) patterns onto the top surface of GaN-based LEDs. When the 280-nm-thick p-GaN was partly etched to ~140 nm, the maximal extraction-efficiency was observed without deteriorating electrical properties. After epoxy encapsulation, the light output of the PC LED was enhanced by 25% in comparison to the standard LED without pattern, at a standard current of 20 mA. By three-dimensional finite-difference time-domain method, we found that the extraction efficiency of the LED tends to be saturated as the etch-depth in the GaN epitaxial-layer becomes larger than the wavelength of the guided modes.