Industrial robots endure severe vibrations in the grinding process due to factors such as joint flexibility, low damping, and contact force fluctuations. Additionally, the motion control of the robot primarily relies on feedback signals from the motor-side encoders, while lacking motion state feedback from the load side. This exacerbates the robot vibrations, severely compromising the surface quality of the workpieces. To address this problem, an active damping control method for robotic grinding using six-axis acceleration feedback is proposed. This method realizes a simple, reliable, and efficient active vibration control without altering the robot body. A multi-sensor fusion Cartesian space six-axis accelerometer is designed and integrated into the robot end effector, achieving accurate feedback on the robot load side vibration state. The strategy of six-axis acceleration decoupling and principle of the vibration suppression with the acceleration feedback are explained. Compared with conventional sensing schemes, this reduces joint acceleration approximation errors and end vibrations. The robotic grinding experiments are carried out on aeronautic structural parts. Extensive case studies demonstrate that the proposed approach can effectively control the vibration caused by joint flexibility in the robot grinding process, and greatly improve the surface quality of workpieces. This method has great potential application in vibration suppression during robotic grinding and polishing.