GaN/AlGaN single quantum disks on GaN nanorods were grown on Si (001) substrate with native SiO2 layer by a plasma-assisted molecular-beam epitaxy under nitrogen-rich conditions. The transmission electron microscopy observations show single GaN nanorods images with an average thickness of 4 nm for the GaN single quantum disk and nanorod diameter of 15 nm. The observed photoluminescence spectra at 8 K show a peak at 3.475 eV, attributed to an exciton recombination in GaN. A strong peak was observed at 3.542 eV. This peak is attributed to the quantum connement of excitons in the GaN quantum disks.