The speed and acceleration planning of the traditional 3-5-3 polynomial interpolation trajectory planning algorithm is too conservative, which is far from the motion limit conditions of the manipulator, and does not give full play to its motion performance, which leads to the increase of the time for the manipulator to complete the task. To solve the above problems, this paper proposes a 3-5-3 polynomial interpolation trajectory planning algorithm based on improved PSO-GSA algorithm. Firstly, the adaptive inertia weight and dynamic learning factor are introduced to improve the PSO-GSA algorithm, and then the improved algorithm is used to optimize the time of 3-5-3 polynomial interpolation algorithm. In the optimization process, the particle group with overspeed used a different fitness function than the one without overspeed, which led the particle group to move closer to the direction of the joint speed decrease, and accelerated the convergence speed of the algorithm. The simulation results show that the improved PSO-GSA algorithm has faster convergence speed, higher search accuracy and is not easy to fall into local optimum than the original algorithm and some similar algorithms. The running time of the 3-5-3 polynomial interpolation trajectory planning method is reduced by 22.9% compared with that before optimization. The obtained trajectory meets the speed limit and is smooth and stable, and the operation is safer and more efficient.