To improve the quality and efficiency of robot grinding, a design and a control algorithm for a robot used for grinding the surfaces of large, curved workpieces with unknown parameters, such as wind turbine blades, are proposed herein. Firstly, the structure and motion mode of the grinding robot are determined. Secondly, in order to solve the problem of complexity and poor adaptability of the algorithm in the grinding process, a force/position hybrid control strategy based on fuzzy PID is proposed which greatly improves the response speed and reduces the error of the static control strategy. Compared with normal PID, fuzzy PID has the advantages of variable parameters and strong adaptability; the hydraulic cylinder used to adjust the angle of the manipulator can control the speed offset within 0.27 rad/s, and the grinding process can be carried out directly without obtaining the specific model of the surface to be machined. Finally, the experiments are carried out, the grinding force and feed speed are maintained within the allowable error range of the expected value, and the results verify the feasibility and effectiveness of the position tracking and constant force control strategy in this paper. The surface roughness of the blade is maintained within Ra = 2~3 μm after grinding, which proves that the grinding quality meets the requirements of the best surface roughness required for the subsequent process.