We grow GaN on MgO substrate by plasma-assisted molecular beam epitaxy (MBE). It is revealed that hexagonal GaN grows on (1 1 1) MgO substrate and cubic GaN grows on (0 0 1) MgO substrate according to the symmetry of the substrates. Mixture of hexagonal phase into cubic GaN is found to be formed in the growth on (0 0 1) MgO, and is investigated by reciprocal space mapping. We obtained GaN epitaxial films with flat surface morphology and good crystalline quality on (1 1 1) MgO substrate. (c) 2006 Published by Elsevier B.V.