A set of ZnO/Mg0.12Zn0.88O multiple quantum wells (MQWs) with well widths, L-w, varying from 6.91 to 46.5 Angstrom has been grown by laser molecular-beam epitaxy. We estimated the L-w dependence of the radiative and nonradiative recombination times of localized excitons at 5 K. Suppression of quantum efficiency can be avoided even in the MQWs having small L(w)s studied in this work. Effects of excitonic localization are discussed in order to explain the L-w dependence of radiative recombination time at 5 K.