Accurate hydrologic time-series prediction plays an important role in modern water resource planning, water supply management, environmental protection, and power system operation. In general, single-layer feedforward networks (SLFNs) can provide satisfactory forecasting results, but classical gradient-based learning algorithms are time consuming and easily trapped into local optimums. As a new training method for SLFNs, extreme learning machine (ELM) has faster training speed and stronger nonlinear mapping than gradient-based algorithms, and provides an effective technique for hydrologic time-series prediction. However, ELM may converge to local minimums in some cases due to the random determination of input weights and hidden biases. Thus, in order to overcome the shortcomings of ELM, this paper introduces a novel ELM–quantum-behaved particle swarm optimization (QPSO) model (ELM-QPSO) combining the advantages of ELM and QPSO. The proposed model adopts the QPSO algorithm to select the optimal input-hidden weights and hidden biases of ELM, and uses the Moore–Penrose generalized inverse to analytically determine the output weights. The proposed approach is assessed with daily runoff data of Xinfengjiang reservoir in China from January 1, 2000 to December 31, 2014. The results indicate that the ELM-QPSO can significantly improve the generalization performance of ELM for hydrologic time-series prediction, and that QPSO is an alternative training algorithm for ELM parameters selection.