In this paper, a new impedance force control method for deburring and polishing process is proposed. The proposed method is robust to deal with unknown environment stiffness as unknown well as environment location. An adaptive technique is used to minimize the force error occurred due to unknown environment surface profile. A robust position control algorithm based on time-delayed information is used to cancel out uncertainties in robot dynamics. A three link robot manipulator is used to demonstrate performances of the proposed control on deburring and polishing tasks. Stability analysis for the adaptive control is presented and its results are confirmed by simulations.