Transient stability assessment (TSA) has always been one of the most challenging problems in power system security and operations due to the rapid growth of electricity demand. The transient stability of power systems should be taken in advance to maintain the system stable. In recent years, a variety of Artificial Intelligence (AI) methods have been applied to the transient stability analysis, including Artificial Neural Network (ANN), Support Vector Machine (SVM) and some other technologies. In this paper, a transient stability prediction method using Long Short-term Memory (LSTM) network based Recurrent Neural Network (RNN) is discussed. Case studies using Multi-layer SVM on the IEEE 9 bus system is adopted as a benchmark to validate the proposed method. Then, the method is performed on the New-England 39 bus system to test the validity. The training and testing data of the LSTM network for the new approach are obtained by performing the time-domain simulation (TDS) on the New-England 39-Bus System in PSAT (Power System Analysis Toolbox) toolbox. Simulation results show that the proposed method exhibits significantly better classification accuracy on predicting the stability, which demonstrates the effectiveness of the proposed approach.