The high-precision forecasting of wind speed is of great significance for the wind power exploitation. In this study, a new hybrid model is presented, which combines the EWT (Empirical Wavelet Transform) decomposition, the GWO (Grey Wolf Optimizer) algorithm, the RELM (Regularized Extreme Learning Machine) network and the IEWT (Inverse Empirical Wavelet Transform) reconstruction. In the proposed structure, to realize the high-precision wind speed prediction, the hybrid modeling strategy has been used as: the EWT is adopted to decompose the raw series into several wind speed subseries adaptively; the RELM network optimized by GWO is employed to forecast each subseries; At the end of the forecasting computation, the IEWT is utilized to reconstruct the forecasted results to avoid the unexpected forecasting values. To evaluate the performance of the proposed model, eleven models are implemented in four forecasting experimental cases. The experimental results of four metrics show that: (1) the IEWT is effective in improving the accuracy and stability of the prediction; (2) the GWO improves the forecasting performance of the proposed hybrid EWT-RELM-IEWT structure significantly; (3) the performance of the RELM network is better than that of the SVM (Support Vector Machine) in the proposed hybrid EWT-GWO-IEWT structure; (4) in the involved forecasting models, the proposed hybrid model has the best multiple step prediction performance.