Dislocation-free vertical GaN pillars in nanoscale were grown on Si (111) surface through self-assembly by molecular-beam epitaxy. No extra catalytic or nanostructural assistance has been employed. These nanorods have a lateral dimension from less than or similar to10 nm to similar to800 nm and a height of less than or similar to50 nm to greater than or similar to3 mum protruding above the film, depending on the growth parameters. The top view of the nanorods has a hexagonal shape from scanning electron microscopy. Transmission electron microscopy shows that the nanorods are hexagonal, single crystal GaN along the c-axis. An extra peak at 363 nm originated from nanorods was observed in photoluminescence spectra at 66 K, which is ascribed to the surface states according to the results of surface passivation. Micro-Raman spectroscopy on a single nanorod reveals E-1 and E-2 modes at 559.0 and 567.4 cm(-1), respectively. Large strain was observed in both the transmission electron micrograph and the Raman shift. A possible growth mechanism is discussed. (C) 2003 American Institute of Physics.