Accurate and prompt transient stability prediction is one of the effective ways to reduce the risk of blackout or cascading failures. In an effort to achieve improvements in time efficiency and prediction accuracy, a new transient stability prediction method combining trajectory fitting (TF) and extreme learning machine (ELM) based on two-stage process, named hybrid method, is proposed here. ELM-based method is implemented in central station to ensure the time efficiency, while TF-based method is adopted in local station to guarantee the accuracy. Furthermore, data corruption is taken into consideration to assure the robustness of the proposed algorithm. The hybrid method is validated with the New England 39-bus test system and the simulation results indicate its effectiveness and reliability.