Transmission electron microscopy and high resolution X-ray diffraction were applied to characterize the crystal structure and its modification in c-InN layers on GaAs (001) substrates grown by rf-plasma assisted molecular beam epitaxy. The layer quality was shown to depend on growth conditions, namely In- and N-rich conditions. The best quality of c-InN layers was achieved by “stoichiometric” growth under the In-rich condition, resulting in In-rich layers with a small amount of hexagonal-phase inclusion (∼8%). On the other hand, nucleation and growth of N-rich layers are shown to result in a high density of stacking faults which drastically decreases toward the InN surface. It is argued that the presence of stacking faults contributes to the structural modification in these layers. We found that the existence of a structural modification from cubic to mixed cubic/hexagonal phase in microstructure of the N-rich layers exhibit higher hexagonal-phase incorporation than that of the In-rich layers.