Abstract The external quantum efficiency of a light-emitting diode (LED) is strictly limited by total internal reflection and Fresnel reflection effects. In this study, we sought to optimize light extraction by monitoring the shape effects of four kinds of periodic textured structures (nanorod, inverted rod, pyramid, inverted pyramid) on the surface of gallium nitride (GaN)-based LEDs. We employed the three-dimensional rigorous coupled waves approach to calculate the direct emissions at different incident angles on the various textured structures, and then determined an optimized structure that would improve the extraction efficiency of LEDs. The optical gradient of the inverted pyramid structure could decrease not only the Fresnel reflection at incident angles less than the critical angle but also the total internal reflection at incident angles greater than the critical angle. Many inverted pyramid structures at the GaN–air interface, with various sizes and periods, provided enhancement factors of greater than 150%.