In order to solve the problem of constant force control in the robot grinding process of a centrifugal pump housing a circular inner surface, this study used the force–position hybrid control mode based on a pneumatic servo system to realize the constant control of grinding force. In this process, the manipulator realizes the position and pose control of the end grinding device, and the end grinding device realizes the constant force control in the grinding process. The mathematical model of the pneumatic system is established and linearized by using the gas balance state equation, the adiabatic equation of the isentropic process, and the Sanville flow equation. The balance equation of the cylinder piston was established by using Newton’s second law, the transfer function of the contact force between the grinding device and workpiece was obtained, and the stability of the pneumatic control system was determined by the Hurwitz criterion. The PID algorithm was used to improve the displacement response speed of the system and eliminate the impact and oscillation in the force response. The feasibility, stability, and robustness of the system were verified by simulation experiments. This method has the advantages of simple control, a small amount of calculation, and a fast response, as well as providing a feasible scheme for the popularization and application of robot grinding technology.