Given the problem caused by the randomness and volatility of wind power under time series, a hybrid wind power forecasting model based on a Self-Adaptive Intelligence Grey Predictive Model with Alterable Structure (SAIGM) and Genetic Algorithm Optimized Kernel Extreme Learning Machine (GA-KELM) is proposed. First, the influence of wind vector and Numerical Weather Prediction (NWP) on wind power in different seasons is analyzed by grey correlation, and the wind speed is predicted by an adaptive intelligent grey system. The predicted wind speed is effectively integrated with the actual wind vector and NWP in the adjacent time series as prediction samples. Secondly, the optimized kernel extreme learning machine based on a genetic algorithm is used to build the wind power prediction model, and the actual wind vector with NWP are also effectively integrated as training samples of the forecasting model. Finally, the optimized prediction model is used to achieve wind power forecasting in different seasons. Experiments demonstrate that the hybrid forecasting model can realize short-term wind power forecasting and the results are accurate and reliable. This work is supported by National Natural Science Foundation of China (No. 61973138).