Due to the unstable contact force during robot grinding results in an inconsistent material removal rate and leads to poor surface quality and reduced machining accuracy. In this work, an independently controlled grinding end-effector was designed to improve the cutting stability and maintain a constant contact force during the robot grinding process. To reduce the influence of vibration force noise on the measurement data and reduce the complexity of the control system, an online estimation method of external grinding force based on generalized momentum is proposed. To keep the grinding force stable, a robot grinding dynamics model and a grinding contact force compensation model are developed, and a variable impedance grinding control strategy without considering the stiffness of work piece is proposed to maintain a consistent normal grinding force and guarantee the stability of material removal rate. Finally, an experimental study was conducted to evaluate the effectiveness of this robotic grinding system. The experimental results show that the force estimator can accurately estimate the grinding contact force, as well as the proposed robot grinding system works well for different work piece contours while maintaining consistent normal grinding force, and the relative average roughness is reduced by 38%.