We report on AlGaN multiple-quantum-well light-emitting diodes over sapphire with peak emission at 325 nm. A pulsed-atomic-layer-epitaxy growth process was used to improve the material quality of the AlN buffer and the AlN/AlGaN strain-relief layers for reducing the nonradiative recombination. In addition, a modified device epilayer structure was used to improve the carrier confinement and the hole injection. A 40% improvement of external quantum efficiency is obtained, resulting in record high optical powers of 10.2 mW at a pulsed pump current of 1 A.