Accurate wind speed prediction reduces the risk of wind speed intermittence and instability to the power system. A hybrid model combined double decomposition technique with RBF (Radial Basis Function) Neural Network is designed to refine the accuracy of the prediction of wind speeds. Firstly, the decomposition technique of ICEEMDAN is introduced to break down the original wind speed, and the decomposition parameters are optimized by BWO (the beluga whale optimization). The decomposed subsequence of the highest frequency is further decomposed by EWT (empirical wavelet transform), reducing the complexity of the sequence. Then the RBF prediction model is adopted to predict each subsequence. The ultimate results are constructed through the aggregation of predictions made for each segmented subsequence. In order to validate the accuracy and stability of the proposed method of BWO-ICEEMDAN-EWT-RBF, the prediction results are compared with the other kinds of models, i.e. BP, LSTM, RBF, CEEMDAN-RBF, ICEEMDAN-RBF and EWT-RBF. The results show that: (a) with the aid of the double decomposition technology of BWO-ICEEMDAN-EWT, the proposed hybrid algorithm effectively reduce the sequence complexity and improve the prediction performance; (b) the model in question substantially boosts the level of precision and stability in the prediction of wind speeds.