Trajectory sensitivity is an important tool for power system dynamic security analysis.A new trajectory sensitivity calculating method based on trajectories for a multi-machine power system is proposed.The mathematical relationship between trajectory sensitivity and trajectory in a power system is constructed based on detailed power system models，and the trajectory sensitivity calculating method based on trajectory is proposed，with the sensitivity of trajectory to parameters directly obtained by the convolution of trajectories alone.The New England10-generator39-bus machine system simulation studies show that the proposed trajectory sensitivity calculating method is valid.The trajectory-based trajectory sensitivity calculating method has revealed the physical association between the trajectory sensitivity and trajectory in power system.And the accuracy of calculating the output is independent of the validity of parameters，providing a new measure for trajectory-based power system dynamic security assessment.