Vertical hexagonal GaN nanorods are grown on (111)Si substrates by plasma-assisted molecular beam epitaxy. No extra catalyst is used to assist the GaN nanorods growth. Nanorods top surfaces are hexagons with diameter less than or equal to10-200 nm by field emission scanning electron microscopy. The image of high-resolution transmission electron microscopy (HR-TEM) shows that the nanorods are single crystal without dislocations. Diffraction pattern of TEM also shows that the nanorods are wurtzite GaN with direction [0001] along the length direction. The temperature dependent photoluminescence (PL) spectroscopy shows only one peak at 3.405 eV at room temperature but two peaks at 3.467 eV and 3.433 eV at 66 K. After ammonia sulfur ((NH4)(2)S) treatment, the low energy peak disappears. The PL spectra are also compared to the ones of epitaxial GaN thin film on (111)Si and it concludes that the low energy peak is from the nanorods contribution. The micro-Raman spectroscopy shows Stokes scattering lines at 532.7 cm(-1), 558.3 cm(-1), 567.1 cm(-1), and 736.1 cm(-1) with 532 nm laser focused on the rod lateral surface and at 558.7 cm(-1), 567.8 cm(-1), and 736.4 cm(-1) focused on the film from the top. The width and the length of the nanorods vary with the growth time and the nanorods growth rate keeps similar to20 % higher than the film. The growth mechanisms will be discussed.