A fast learning method to predict the rotor angles of the generators to be considered as losing synchronism is proposed. The method adopts a widely used robotic ball-catching algorithm based on a continual stream of accurate generator rotor angle data measured by phasor measurement unit（PMU） on line. The method is divided into two parts. The tracking process is improved by the use of particle swarm optimization（PSO） to perform multi-parameter optimization. Meanwhile， the prediction process uses the Taylor series expansion to predict the generator rotor angle. The algorithm does not require prior knowledge of the system configuration and is able to predict the stability of the generators 500 milliseconds into the future and to save enough“action time” for on-line instability alarm and local control. The simulation results on the 10-generator， 39-bus New England Test System and 50-machine， 145-bus test system demonstrate the effectiveness of the proposed method for transient stability prediction.