Forecasting wind speed accurately is a key task in the planning and operation of wind energy generation in power systems, and its importance increases with the high integration of wind power into the electricity market. This research proposes an innovative hybrid model based on optimal feature extraction, deep learning algorithm and error correction strategy for multi-step wind speed prediction. The optimal feature extraction including variational mode decomposition, Kullback-Leibler divergence, energy measure and sample entropy is utilized to catch the optimal features of wind speed fluctuations for balancing the calculation efficiency and prediction accuracy. The deep learning algorithm based on long short term memory network, is utilized to detect the long-term and short-term memory characteristics and build the suitable prediction model for each feature sub-signal. The error correction strategy based on a Generalized auto-regressive conditionally heteroscedastic model is developed to modify the above prediction errors when its inherent correlation and heteroscedasticity cannot be ignored. Three real forecasting cases are applied to test the performance and effectiveness of the developed model. The simulation results indicate that the developed model consistently has the smallest statistical errors, and outperforms other benchmark methods. It can be concluded that the developed approach is conductive to strengthening the prediction precision of wind speed.