Short-term wind speed prediction is of cardinal significance for maximization of wind power utilization. However, the strong intermittency and volatility of wind speed pose a challenge to the wind speed prediction model. To improve the accuracy of wind speed prediction, a novel model using the ensemble empirical mode decomposition (EEMD) method and the combination forecasting method for Gaussian process regression (GPR) and the long short-term memory (LSTM) neural network based on the variance-covariance method is proposed. In the proposed model, the EEMD method is employed to decompose the original data of wind speed series into several intrinsic mode functions (IMFs). Then, the LSTM neural network and the GPR method are utilized to predict the IMFs, respectively. Lastly, based on the IMFs’ prediction results with the two forecasting methods, the variance-covariance method can determine the weight of the two forecasting methods and offer a combination forecasting result. The experimental results from two forecasting cases in Zhangjiakou, China, indicate that the proposed approach outperforms other compared wind speed forecasting methods.