How to predict the aging trend of the software accurately, and take the corresponding recovery strategy is a key problem of preventing software aging. To solve the problem, this study designs a resource prediction method based on Recurrent Neural Network (RNN) and its variant-Long Short-Term Memory (LSTM), and builds an accelerated aging test platform to model and forecast the aging phenomenon of the Web server due to memory leak. The experiments show that LSTM network prediction model proves to be superior to the other traditional models in dealing with the time sequence modeling of aging parameters, with the predicted results closer to the actual values and the higher prediction accuracy, which can effectively improve the reliability and availability of the software system.