In order to improve the smoothness and stability of the motion of the cable-driven continuum robot, the trajectory planning methods based on spline function and particle swarm optimization algorithm were proposed for the cable-driven continuum robot in its joint space and Cartesian space respectively. Firstly, the kinematic model was established by applying the local product-of-exponential(POE) formula with two parameters. Secondly, the inverse kinematics was solved by Newton Raphson iterative method. Finally, the particle swarm time optimization algorithm based on adaptive inertia weight combing with the quintic B-spline function was used to realize the trajectory planning of the continuum robot in joint space and Cartesian space respectively. The simulation results show that continuous trajectories can be obtained both in joint space and Cartesian space under the same conditions, the obtained velocities are less than 10 mm/s, and the accelerations are less than 20 mm/s2.The joint displacement, velocity and acceleration curves are smoother in joint space, which takes 9.219 3 s, while it takes 10.604 6 s in Cartisian space. The research on trajectory planning of a cable-driven continuum robot based on particle swarm optimization algorithm improves the kinematic performance of the continuum robot and provides references for pose planning of the cable-driven continuum robots.