The pneumatic soft manipulator is made of flexible materials, which has the characteristics of strong environmental adaptability, safe human-machine interaction, etc. In practice, the pneumatic soft manipulator has more and more applications in medical rehabilitation, aquaculture, pipeline maintenance, search and rescue work, etc. In recent years, the demand for pneumatic soft manipulators has increased, and higher requirements have been put forward for their flexibility and operation accuracy. However, due to the large deformation nonlinear characteristics of the pneumatic soft manipulator, its kinematic modeling is difficult. Considering this fact, this paper focuses on the kinematic modeling and trajectory planning for the pneumatic soft manipulator with three chambers. Firstly, we obtain the forward kinematic and inverse kinematic models of the pneumatic soft manipulator with three chambers through rigorous analysis and mathematical derivation. After that, based on the kinematic model, we propose a trajectory planning method for the pneumatic soft manipulator with three chambers. Finally, simulation results are given to test the satisfactory performance of the proposed method.