We report on photoluminescent properties of ZnO/Zn0.8Mg0.2O nanorod single-quantum-well structures (SQWs). Catalyst-free metalorganic vapor-phase epitaxy (MOVPE) was employed for precise controls of well widths and compositions of the nanorod SQWs. Both time-integrated and time-resolved photoluminescence (PL) spectra of ZnO/Zn0.8Mg0.2O nanorod SQWs were measured at various temperatures between 10 and 300 K. From the PL spectra of the nanorod SQWs measured at 10 K, a PL peak blue-shift dependent on ZnO well layer width was observed, resulting from a quantum confinement effect. Further photoluminescent properties of the nanorod SQWs were investigated measuring time-resolved PL (TRPL) and temperature-dependent PL spectra.