The high-quality grinding of the aviation blade components with the industry robot presents tremendous challenges because of the complexity of blade surface. The hybrid force/position anti-disturbance control strategy is developed base on fuzzy PID control to improve the quality of grinding aviation blades. Firstly, according to gravity compensation technology, the perception of contact force is discussed to solve the contact force between the blades and abrasive belt machine. Then, the hybrid force/position anti-disturbance control strategy is designed to ensure the stability of robot automatic grinding system. The speed gain loop and the dual fuzzy PID control are introduced to enhance the anti-disturbance ability of the control system. Meanwhile, the analysis of stability and steady-state error for force control loop are performed to prove the validation of the feasibility of control system. Eventually, the simulation and experiments are carried out on the robot automatic grinding system. The experimental results reveal that the proposed control strategy can achieve better control effect and grinding quality compared with the traditional PID control.