A set of GaN/AlxGa1-xN(x≈0.2) multiple quantum wells (MQWs) with well widths, Lw, varying from 6 to 48 Å has been grown by metalorganic chemical vapor deposition under the optimal GaN-like growth conditions. Picosecond time-resolved photoluminescence spectroscopy has been employed to probe the well-width dependence of the quantum efficiencies (QE) of these MQWs. Our results have shown that these GaN/AlGaN MQW structures exhibit negligibly small piezoelectric effects and hence enhanced QE. Furthermore, GaN/AlxGa1-xN MQWs with Lw between 12 and 42 Å were observed to provide the highest QE, which can be attributed to the reduced nonradiative recombination rate as well as the improved quantum-well quality. The decreased QE in GaN/AlxGa1-xN MQWs with Lw< 12 Å is due to the enhanced carrier leakage to the underlying GaN epilayers, while the decreased QE in MQWs with Lw> 42 Å is associated with an increased nonradiative recombination rate as Lw approaching the critical thickness of MQWs. The implications of our results on device applications are also discussed.