Wind power has significant randomness. Probabilistic prediction of wind power is necessary to solve the problem of safe and stable power grid dispatching with the integration of large-scale wind power. Therefore, this paper proposes a novel nonparametric probabilistic prediction model for wind power based on extreme learning machine-quantile regression (ELM-QR). Firstly, the ELM-QR models of multiple quantiles are established, and then the new comprehensive index (NCI) is optimized by particle swarm optimization (PSO) to obtain the weighting coefficients corresponding to the lower and upper bounds of the prediction intervals. The final prediction interval is obtained by integrating the outputs of ELM-QR models and the weighting coefficients. Finally, case studies are carried out with the real wind farm operation data, simulation results show that the proposed algorithm can obtain narrower prediction intervals while ensuring high reliability. Through sensitivity analysis and comparison with other algorithms, the effectiveness of the proposed algorithm is further verified.