To improve the accuracy of wind power prediction, a wind power prediction method based on Bayesian optimization variational mode decomposition (VMD) and a gated recurrent unit (GRU) is proposed. First, the VMD algorithm is used to decompose the wind power sequence, and the optimal mode number of sequence decomposition is determined according to the size of permutation entropy (PE). Then, the decomposed sub-sequence components are combined with the key meteorological variable data to form the input characteristics of the model. The GRU network is used to predict each sub-sequence component separately, and the prediction results of each sub-sequence component are reconstructed to obtain the wind power prediction results. Finally, the Bayesian optimization method is used to optimize the network initial hyperparameters of each subsequent prediction model. The proposed model is evaluated on a real wind power data from a wind farm and compared with six baseline models. The results show that the VMD-GRU prediction model based on Bayesian optimization is clearly the superior model, has better generalizability, and can effectively improve the prediction accuracy of wind power.