We have investigated effect of the In- and N-rich growth conditions on the structural modification of cubic-phase InN (c-InN) films grown on GaAs (001) substrates by rf-plasmaassisted molecular beam epitaxy (RF-MBE). High resolution x-ray diffraction (HRXRD) and Raman scattering measurements were performed to examine the hexagonal phase generation in the c-InN grown films. It is evident that higher crystal quality c-InN films with higher cubic phase purity (~82%) were achieved under the In-rich growth condition. On the other hand, for the N-rich growth condition, the c-InN films exhibited higher incorporation of hexagonal phase, which is generated in the cubic phase through the incidental stacking faults on the c-InN (111) planes. Our results demonstrate that the In-rich growth condition plays a critical role in the growth of high quality c-InN films with higher cubic phase purity.