We demonstrate GaN-based blue light-emitting diodes (GaN LEDs) with artificial compound eye structures (CESs). The GaN LEDs consist of microlens arrays (MLAs) and antireflective subwavelength structures (SWSs). The CESs, formed on the LED surface by two-step pattern transfer of reflowed photoresist micro patterns and Ag nanoparticles, play an important role in enhancing the light extraction efficiency by reducing both the Fresnel and the total internal reflection. The CES integrated GaN LEDs show an output power enhancement of 93% compared to that of conventional GaN LEDs with flat surface, without any serious degradation of electrical characteristics. Optical simulations by ray-tracing and the rigorous coupled-wave analysis method provide design guidelines for MLAs and SWSs, respectively.