The characteristics of single‐crystal GaN regions obtained by selective‐area and subsequent lateral overgrowth on stripe‐patterned GaAs (001) substrates by MOVPE were studied. Under certain growth conditions, the surface kinetics of the MOVPE process result in lateral‐growth of both hexagonal‐GaN (h‐GaN) and cubic‐GaN (c‐GaN) stripes with the appropriate mask stripe orientation, namely [110] and [1$ \bar 1 $0], respectively. The facet structure comprises the c‐GaN stripes surrounded with (111) B facets and mixture facets of (311) A, (111) A, and an inversed (111) B for the stripe window opening along the [110] and [1$ \bar 1 $0] directions, respectively. The cross‐sectional TEM micrographs showed that the h‐GaN is laterally overgrown along the (111) B facets of the c‐GaN stripes. For the [110]‐stripes, the laterally overgrown h‐GaN regions contained a very low density of dislocations (<108 cm—2). On the other hand, for the [1$ \bar 1 $0]‐stripes, a large reduction of stacking fault density was found in the overgrown c‐GaN regions. We demonstrated that both high quality h‐GaN and c‐GaN films were successfully grown on the stripe‐patterned GaAs (001) substrates by MOVPE.