Crystalline quality of cubic phase (c-) GaN epilayers on (0 0 1) GaAs has been systematically investigated by varying nitrogen (N-) beam direction in molecular beam epitaxy. In this study, the N-beam was obliquely incident to the surface normal. The N-beam direction during both buffer layer and epilayer depositions could approximate either c-GaN[1 1 1]A or c-GaN[1 1 1]B. In the c-GaN epilayers grown with different N-beam directions, the c-GaN domain or hexagonal (h-) GaN domain showed the tilt and the mosaicity. From the X-ray rocking curves, the extraordinary c-GaN domains and the h-GaN domains were tilted by influence of oblique incidence of the N-beam. The phase purity of c-GaN domain became high when the N-beam direction was along a c-GaN[1 1 1]A direction during both the buffer layer and the epilayer depositions. In order to understand the difference in crystalline quality with change in the N-beam direction, we took account of stack of the Ga and N precursors on (1 1 1)A (or ((1) over cap 1 1)B) c-GaN facet. It is considered that the difference of the crystalline quality result from the polarity of the facets.