An adaptive algorithm for the detection of burrs and cavities on a workpiece is proposed for the beburring process. The conventional force control method for the deburring process has the inherent characteristic of leaving the deburred surface or edge as an imprint of the original and can not distinguish the position deflection of the end-effector and the larger burrs. By the adaptive algorithm, the reference cutting force in normal direction and the feed-rate can be adjusted automatically according to the variation of the burr size to get smooth surface. A process force model considering the burrs effect is developed to predict the cutting force. Furthermore, the proposed algorithm is integrated into the impedance control for the deburring operation. The simulation experiment has shown that the adaptive algorithm is effective to determine the existence of the burrs, obtain the desired contour and improve the machining efficiency.