High-quality cubic GaN epilayer on GaAs(0 0 1) was grown by molecular beam epitaxy equipped with radio frequency nitrogen source. The optimized growth condition is to grow two monolayers thick initial GaN at 600 degrees C under As atmosphere. X-ray diffraction rocking curve shows that the full-width at half-maximum of cubic GaN(0 0 2) diffraction peak is 10 arcmin. The X-ray reciprocal space mapping is used to identify the secondary hexagonal phase and estimate their relative content.