We demonstrate the fabrication of hexagonal nano-pillar arrays at the surface of GaN-based light-emitting diodes (LEDs) by nanosphere lithography. By varying the oxygen plasma etching time, we could tune the size and shape of the pillar. The nano-pillar has a truncated cone shape. The nano-pillar array serves as a gradual effective refractive index matcher, which reduces the reflection and increases light cone. It is found that the patterned surface absorbs more pumping light. To compare extraction efficiencies of LEDs, it is necessary to normalize the photoluminescence power spectrum with total absorption rate under fixed pumping power, then we could obtain the correct enhancement factor of the photoluminescence extraction efficiency and optimized structure. The highest enhancement factor of the extraction efficiency is 10.6.