In the prediction of engine remaining life (RUL), the data feature extraction is easy to lead to low prediction efficiency. To solve this problem, an improved algorithm model of long short-term memory (LSTM) was proposed. The sparse deep autoencoder (SDAE) method was introduced to process the time series data and optimize the LSTM model, and the RUL prediction effect of aeroengine was improved. SDAE was used for feature extraction, and the health indicator (HI) curve was constructed; three factors including operating condition, fault mode and sensor were all considered, and their weights were trained respectively. LSTM model was used to predict the remaining life. The turbo-fan degradation process data set C-MAPSS was used to carry out experiments, and compared with DNN, BILSTM and single-layer LSTM. The results show that compared with the above three alogrithms,the RMSE error and the scoring function value of the improved algorithm are decreased by at least 6.6% and 39.1% respectively; the life prediction results of this method and the actual life curve have a high fitting degree, and the feasibility and effectiveness of this method are verified.