We have fabricated GaAs nanodisk (ND) structures by using a combination of neutral beam etching process and atomic hydrogen-assisted molecular beam epitaxy regrowth. We have observed clear photoluminescence (PL) emissions from GaAs NDs. The peak energy showed a blueshift due to the quantum confinement in three spatial dimensions, and it agreed with the theoretically estimated transition energy. The PL results also showed that the cap-layer disks act as radiative recombination centers. We have confirmed that the PL emission originates from the GaAs NDs, and our approach is effective for the fabrication of high quality ND structures.