Wind speed interval prediction is of great significance in power resource scheduling and planning. However, the complex and variable characteristics of wind speed make quality forecasting challenging. In this paper, a novel hybrid model, abbreviated as RSAE-LSTM, for wind speed interval prediction is proposed. The model employs a rough stacked autoencoder (RSAE) and long short-term memory neural network (LSTM). The RSAE initially handles uncertainties and extracts important potential features from the wind speed data. Then, the generated features are utilized as input to the LSTM network to construct the prediction intervals (PIs). Meanwhile, a new loss function is proposed for developing model to construct PIs effectively. The experimental results show that compared with the comparison methods, the proposed method could obtain high-quality PIs and achieve at least a 39% improvement in the coverage width criterion (CWC) index.