Display omitted •A new WPD-FEEMD-Elman method is proposed for the wind speed predictions.•A new secondary algorithm is presented for the wind speed decomposition.•The FEEMD algorithm is adopted in the hybrid decomposition.•The Elman neural network is employed in the hybrid forecasting. Wind speed forecasting technology is important in the field of wind power. However, the wind speed signals are always nonlinear and non-stationary so that it is difficult to predict them accurately. Aims at this challenge, a new hybrid approach has been proposed for the wind speed high-accuracy predictions based on the Secondary Decomposition Algorithm (SDA) and the Elman neural networks. The proposed SDA combines the Wavelet Packet Decomposition (WPD) and the Fast Ensemble Empirical Mode Decomposition (FEEMD), which includes twice decomposing processes as: (a) the WPD decomposes the original wind speed into the appropriate components and the detailed components; and (b) the FEEMD further decomposes the WPD generating detailed components into a number of wind speed Intrinsic Mode Functions (IMFs). The experimental results in five real forecasting cases show that: (a) the proposed hybrid WPD-FEEMD-Elman model has satisfactory performance in the multi-step wind speed predictions; and (b) the hybrid WPD-FEEMD-Elman model has improved the forecasting performance of the hybrid WPD-Elman model and the standard Elman neural networks considerably.