How to predict wind speed with high accuracy is a fundamental issue for the generation of wind power and energy management of power systems. Moreover, the nonlinear and non-stationary characteristics of wind speed make the task extremely challenging. To resolve this issue, a novel hybrid interval prediction model based on long short-term memory (LSTM) networks and variational mode decomposition (VMD) algorithm is developed in the frame of lower upper bound estimation in this study. Firstly, VMD is applied to decompose sequences of raw wind speed into several different modal components containing different information. Then, a LSTM-based model for each component is built to predict the corresponding wind speed information. In the LSTM structure, lower and upper bounds of the prediction intervals (PIs) are constructed and two customized cost functions based on the probability of convergence and width of the PIs are proposed to optimize the model with gradient descent algorithm. Additionally, particle swarm optimization (PSO) is applied to optimize the hyperparameters in the two cost functions of each LSTM. Finally, experiments with different scales of datasets were conducted to show the feasibility and effectiveness of the proposed method by comparing it with traditional methods. The results demonstrate that the proposed model yielded significantly superior performance with a clear enhancement in the PI quality.INDEX TERMS Interval prediction, wind speed forecasting, long short-term memory networks, variational mode decomposition, lower upper bound estimation, particle swarm optimization, customized cost function.