Abstract: An original exciting force index can describe vibration of flexible space robot is proposed for the first time. The exciting-force index can be calculated directly by the trajectory. Then a trajectory planning algorithms of flexible space robot for vibration reducing is proposed. Describing trajectory with fourth-order quasi-uniform B-spline, the planning algorithms can be realized by using a proved Particle Swarm Optimization method to calculate the control point parameter of B-spline. The planning efficiency is extremely improved by replacing the control result with exciting-froce index to judge an undetermined trajectory. A simulation on a flexible dual-arm space robot that contrasted an optimized trajectory with a simple cubic polynomial one and got much less vibration has shown the effectiveness of the algorithms.