We grew GaN crystals by metalorganic vapor phase epitaxy on (111) and (100) MgAl2O4 substrates. We obtained a single-crystal GaN layer with a specular surface on the (111) substrate. The full width of half-maximum of the x-ray rocking curve for a 3.6 μm thick GaN layer was 310 s, comparable to the reported values for GaN on Al2O3 substrates. In the room-temperature photoluminescence, a band-edge emission at around 360 nm was dominant. A smooth cleaved (11̄00) facet of the GaN epitaxial layer was obtained, assisted by the inclined (100) cleavage of the (111) MgAl2O4 substrate. We intend this cleaved facet, which is normal to the surface, to be used as a cavity mirror in a laser diode.