Big multi-step wind speed forecasting is hard to be realized due to the high-requirement of the built forecasting models. However, the big multi-step forecasting is expected in the wind power systems, which can provide sufficient time for the wind grids to be operated in the emergency cases. In the study, a new hybrid computational framework for the big multi-step wind speed forecasting is proposed, consisting of Wavelet Packet Decomposition (WPD), Elman Neural Networks (ENN), boosting algorithms and Wavelet Packet Filter (WPF). The novelty of the study is to investigate the big multi-step wind speed forecasting performance using various computing strategies in the proposed new hybrid WPD-BoostENN-WPF framework. Four different wind speed time series data are provided to complete the real forecasting experiments. The experimental results indicate that: (a) all of the proposed hybrid models have better performance than the corresponding single forecasting models in the big multi-step predictions. The 9 step MAE errors for the experimental data #1 from the proposed four hybrid forecasting models are only 1.2821 m/s, 1.1276 m/s, 1.1718 m/s and 1.2684 m/s, respectively; (b) the proposed four hybrid forecasting models have no significant forecasting difference; and (c) all of them are suitable for the big multi-step wind speed forecasting. (C) 2018 Elsevier Ltd. All rights reserved.