We present photoluminescence (PL) and time-resolved photoluminescence measurements in GaN/Al0.2Ga0.8N superlattices grown by metalorganic chemical vapor deposition under the optimal GaN-like growth conditions. We found that the carrier confinement of our samples is better than most of the previous reports. The dependence of the PL emission energy and intensity on temperature, in the low temperature regime, is consistent with recombination mechanisms involving localized states attributed to a small degree of interface fluctuations. Picosecond time-resolved photoluminescence spectroscopy has been employed to probe the well-width dependence of the lifetime of these superlattices. We see that the recombination lifetime increases with the decrease of well width. This behavior can be interpreted by the fact that the effect of localization keeping carriers away from nonradiative pathways can be enhanced by a decrease in the well width. This explanation is consistent with the temperature-dependent PL data.