With the development of smart healthcare, surgical and rehabilitation robots have permeated into daily medical operations. This raises concerns over the trajectory planning of medical manipulators. Based on particle swarm optimization (PSO) algorithm and fuzzy neural network (FNN), this paper puts forward a trajectory planning algorithm for medical manipulators, which ensures that the target medical manipulator can suppress the residual jitter at the end, while meeting the requirements of high precision, flexible operation, and disturbance resistance. Specifically, a kinetic model was constructed for a medical manipulator of multi-degrees-of-freedoms (DOFs) through position and posture transforms, and used to construct an FNN for trajectory planning. To suppress the jitter at the end, an adaptive PSO algorithm was designed, and combined with the FNN into a trajectory planning algorithm called PSO neural network (PSONN) algorithm. Finally, the proposed algorithm was proved effective through experiments. The research results provide the reference for applying PSO algorithm and FNN in other fields.