Two InGaN/GaN multiple-quantum-well (MQW) samples with identical epitaxial structures are grown at different growth rates via metal-organic chemical vapor deposition system. The room temperature photoluminescence intensity of the fast-grown sample is much stronger than that of the slow-grown one. In addition, the fast-grown sample has two luminescence peaks at low temperatures, and the height of main peak anomalously increases with increasing temperature below 100 K. Such improved emission efficiency and the untypical temperature-induced increase of peak height can be attributed to the carrier's transferring between two kinds of localized traps with different potential depth in the fast-grown sample, where the distribution of indium is seriously inhomogeneous. The enhanced fluctuation of indium is caused by the reduced migration time of adsorbed atoms due to the increased growth rate during the epitaxial growth of MQW region.