Wind energy, as one of the renewable energies with the most potential for development, has been widely concerned by many countries. However, due to the great volatility and uncertainty of natural wind, wind power also fluctuates, seriously affecting the reliability of wind power system and bringing challenges to large-scale grid connection of wind power. Wind speed prediction is very important to ensure the safety and stability of wind power generation system. In this paper, a new wind speed prediction scheme is proposed. First, improved hybrid mode decomposition is used to decompose the wind speed data into the trend part and the fluctuation part, and the noise is decomposed twice. Then wavelet analysis is used to decompose the trend part and the fluctuation part for the third time. The decomposed data are classified. The long- and short-term memory neural network optimized by the improved particle swarm optimization algorithm is used to train the nonlinear sequence and noise sequence, and the autoregressive moving average model is used to train the linear sequence. Finally, the final prediction results were reconstructed. This paper uses this system to predict the wind speed data of China’s Changma wind farm and Spain’s Sotavento wind farm. By experimenting with the real data from two different wind farms and comparing with other predictive models, we found that (1) by improving the mode number selection in the variational mode decomposition, the characteristics of wind speed data can be better extracted. (2) According to the different characteristics of component data, the combination method is selected to predict modal components, which makes full use of the advantages of different algorithms and has good prediction effect. (3) The optimization algorithm is used to optimize the neural network, which solves the problem of parameter setting when establishing the prediction model. (4) The combination forecasting model proposed in this paper has clear structure and accurate prediction results. The research work in this paper will help to promote the development of wind energy prediction field, help wind farms formulate wind power regulation strategies, and further promote the construction of green energy structure.