As a basic model of the grey system theory, the GM(1,1) model has a very wide range of application, which uses the finite samples or poor information. One of its major drawbacks is the low precision in forecasting the long-term sequences. To solve this problem, the residual of the GM(1,1) is used to be optimized by introducing other algorithms which can greatly improve the overall prediction performance. This paper introduces the long short-time memory network to optimize the residuals of the GM(1,1), which can make full use of the nonlinear mapping and its mining ability for time series to achieve higher prediction accuracy. The chronological residual sequence of the GM(1,1) model is processed to generate a new time series that can regard as the initial sequence for long short-time memory network to train and predict the corrected residual. Based on the corrected residual model, the predicting value of the GM(1,1) model is added with the predicting value of the corrected residual sequence to get the ultimate forecasting value. The feasibility and accuracy are verified by one case which shows that the combined model of the GM(1,1) and LSTM network can get the better precision and make up for the defects of the traditional GM(1,1) in processing long complex time series. The application range of the GM (1,1) model is extended to some extent.