We report on a new approach to fabricate regular arrays of GaN nanorods (NRs) with InGaN QWs by plasma-assisted molecular-beam epitaxy (PA MBE) on micro-cone patterned sapphire substrates (mu-CPSSs). A two-stage PA MBE fabrication process of GaN NRs has been developed, starting with a high temperature nucleation layer growth at metal-rich conditions to aggregate selectively GaN nucleus on c-oriented areas of the mu-CPSSs and followed by growth of 1-mu m-thick GaN NRs at strongly nitrogen-rich conditions exactly on the cone tips. These results are explained by energetically favorable GaN growth on the (000 (1) over bar) oriented sapphire surface. Both micro-photoluminescence and micro-cathodoluminescence confirm the formation of regular array of optically and spectrally isolated NRs without usage of any nanolithography.