Wind speed interval prediction plays an important role in wind power generation. In this article, a new interval construction model based on error prediction is proposed. The variational mode decomposition is used to decompose the complex wind speed time series into simplified modes. Two types of GRU models are built for wind speed prediction and error prediction. Prediction error for each mode is given a weight and accumulated to obtain the width of the prediction interval. The particle swarm optimization algorithm is applied to search for the optimal weights of the prediction errors. Experiments considering eight cases from two wind fields are conducted by using methods of interval construction in the literature for comparison with the proposed model. The result shows that the proposed model can obtain prediction intervals with higher quality.