Wind energy is a kind of sustainable energy with strong uncertainty. With a large amount of wind power injected into the power grid, it will inevitably affect the security, stability and economic operation of the power grid. High-precision wind power spot prediction and fluctuation interval information can provide more adequate decision-making support for grid scheduling and optimization. Hence, this paper proposes a K-Means-long short-term memory (K-Means-LSTM) network model for wind power spot prediction, and a nonparametric kernel density estimation (KDE) model with bandwidth optimization for wind power probabilistic interval prediction. The long short-term memory (LSTM) network has a strong memory function, which can establish the correlation between the data before and after, so as to improve the prediction accuracy. The K-Means clustering method forms different clusters of wind power impact factors to generate a new LSTM sub-prediction model. The optimization of the bandwidth in the nonparametric KDE is implemented by the mean integrated squared error criterion. In addition, a part of the dataset is deliberately demarcated from the wind power historical dataset to generate reasonable wind power prediction errors. The simulation results show that the proposed K-Means-LSTM network model has higher prediction accuracy than the back propagation (BP) neural networks, Elman neural networks, support vector regression (SVR) and LSTM network models. Compared with the KDE model with random bandwidth and the Gaussian distribution model, the bandwidth optimization model proposed in this paper has more narrow prediction intervals with higher interval coverage rates. INDEX TERMS Wind power prediction, Kernel density estimation, long short-term memory, K-means clustering, probabilistic interval prediction.