Photoluminescence (PL) properties of a single nanorod containing multiple GaN quantum disks separated by AlGaN potential barriers are investigated using micro-PL spectroscopy. Previous studies reported ensemble spectra from many nanorods. The PL spectra show different features depending on the region of the nanorod excited by the laser, including a sharp feature originating from the quantum disk region. The distinct differences between the PL from the different regions are discussed. The results imply that excitons are strongly confined in the quantum disks, and the authors suggest that small quantum disks can be regarded as quantum dots having a discrete density of states.