Different with traditional rigid robots, cable-driven continuum robots are able to working in the narrow space to realize the inspection or detection. To improve the smoothness and stability of its motion trajectory, the trajectory planning method based on spline and particle swarm is proposed for the cable driven continuum robot in its joint space and Cartesian space. Firstly, the kinematic model has been built by using the two parameters local product-of-exponential (POE) formula, Secondly, the inverse kinematic has been solved by using Newton Raphson iterative method. Finally, the particle swarm optimization algorithm based on adaptive inertia weight has been used to solve the time optimal problem and the B-spline function has been used for generate smoothly trajectory, the trajectory planning of the continuum robot in joint space and Cartesian space is realized respectively. The simulation results show that the planned trajectories both in joint space and Cartesian space are continuous. The obtained velocities are less than 10 mm/s and the accelerations are less than 20 mm/s^2. However, the produced position, velocity and acceleration curves are smoother when doing the trajectory planning in joint space. In terms of running time,it takes 9.219 3 s in joint space planning and takes 10.604 6 s in Cartisian space.