We report a dramatic increase in the internal quantum efficiency (IQE) of ZnO/ZnMgO multi-quantum wells (MQWs) fabricated on c-plane sapphire substrate by introducing asymmetric double-quantum-well (ADQW) structure. A marked enhancement in efficiency, by as much as 1.56 times, was observed for the ZnO/ZnMgO five-period ADQW grown by plasma-assisted molecular beam epitaxy (P-MBE), compared to the ten-period symmetrical MQWs with asymmetric structure. The effects of excitons tunneling from the narrow well to the wide well, which was proved by photoluminescence spectra and time-resolved photoluminescence spectroscopy, can influence the IQE.