It is difficult to predict stock index volatility accurately because of its non-stationary, highly noisy and non-linear, while traditional forecasting models require smooth, linear or approximately linear data in modeling. To improve the forecasting effect of stock index volatility, a model constructed by empirical modal decomposition (EMD), sample entropy (SE) and long short-term memory network (LSTM) is used to forecast the intra-day realized volatility of stock index. Taking the CSI 500 index as an example, a series of components are obtained after EMD decomposition, and are reconstructed according to the sample entropy magnitude of the components, and finally the LSTM is used to forecast each reconstructed series. The results show that the EMD algorithm also improves the prediction accuracy of the LSTM model, and the EMD-SE-LSTM model has higher accuracy and better fit superiority in predicting the stock index volatility compared with the traditional model.