To realize high-efficiency light-emitting diodes (LEDs), it is indispensable to increase light extraction efficiency. We propose the moth-eye structure on the surface of an LED chip, which consists of periodic cones with a pitch of optical wavelength scale, and enables the significantly enhancement of light extraction efficiency. We have developed a new technique for moth-eye structure fabrication, on the basis of low-energy electron-beam projection lithography (LEEPL), which can be applied to the mass production of LEDs. The moth-eye structure formed at the bottom of a SiC wafer has periodically arranged cones with a 300 nm pitch and a 750 nm height. We also present blue LEDs fabricated on SiC substrates with and without the moth-eye structure, and discuss the effect of the moth-eye structure on the performance of LEDs.