Accurate wind speed prediction is a premise that guarantees the reliable operation of the power grid. This study presents a combined prediction model that integrates data preprocessing, cascade optimization, and deep learning prediction to improve prediction performance. In data preprocessing, the wavelet soft threshold denoising (WSTD) is employed to filter the blurring noise of the original data. Then, the robust empirical mode decomposition (REMD) and adaptive variational mode decomposition (AVMD) are adopted to carry out a two-stage adaptive decomposition. Spearman correlation is used to quantify the mode that need to be decomposed for the second time. In the cascade optimization, the hybrid grey wolf algorithm (HGWO) is employed to optimize the parameters of the VMD and the gated recurrent unit (GRU), which overcomes the problem of empirical parameter adjustment. The HGWO is also adopted in the prediction strategy to optimize the GRU model to predict the grouped intrinsic mode functions (IMFs). Lastly, the final wind speed prediction result is obtained by superimposing the values of all the predicted models. The proposed model was validated with the measured wind speed data of the four quarters in the Bay area of China and was compared with 20 models of the classic method to further evaluate the effectiveness of the model. The results show that the whole process of the proposed model is adaptive, the final multi-step prediction performance is good, and high prediction accuracy can be attained.