The growth of high-quality InN nanorods (NRs) on Si (111) by plasma-assisted molecular beam epitaxy (PAMBE) is reported. X-ray diffraction and Raman spectroscopy investigations indicates that the NRs are wurtzite, c-axis oriented and single crystalline. Low temperature photoluminescence emissions with peak energy of ~ 0.75eV was observed indicating the high quality of the nanostructures. This study unravels a novel strategy for the successful growth of high-quality InN NRs on Silicon which is highly promising for applications in next generation nanodevices.