A novel method for perturbed trajectory prediction of post-fault rotor angle is presented in this paper， which is based on phasor measurement unit（PMU） measurements and trigonometric function curve fitting technique. A mathematical relationship of post-fault rotor angle and time is derived from a speed-governing system， which reveals that the perturbed trajectory of the post-fault rotor angle can be expressed by attenuation trigonometric functions. Using curve fitting technique and trigonometric function， a least square method to predict the perturbed trajectory is proposed. Numerical simulations are conducted in IEEE 9-bus system and the simplified north China grid to test the effectiveness of the proposed method. The proposed method can give more reasonable and more promising prediction results as compared with polynomial curve fitting technique.