Accurate wind power prediction is beneficial for power system operation, peak regulation, safety analysis and consumption reduction. A wind power prediction method is proposed based on Long Short-Term Memory (LSTM) combining Robust Regression (RR) and Variational Mode Decomposition (VMD). The RR method is first used to process the missing values and abnormal points of the collected data. Then VMD is proposed to decompose the wind power sequence to eliminate noise and inherit the main characteristics of the original sequence. Finally, LSTM is employed to learn the historical time series of each decomposition sequence and complete the prediction, and all prediction results are integrated to obtain the final prediction of wind power. The proposed method is applied in the wind power prediction of one farm in North China, and the prediction results are compared with other models. The results show that the RR-VMD-LSTM method can significantly improve the prediction performance and reduce the wind power prediction error. This work is supported by the “the 13th Five-Year” National Key Research and Development Program of China (No. 2018YFB1502902) and the Natural Science Foundation of Shaanxi Province (No. 2021JM-378).