To solve the problem that the adaptive adjustment ability of robotic compliant constant force grinding is insufficient due to the complex time-varying nonlinear coupling and uncertainty disturbance in the industrial robot grinding process, a robotic force-controlled end-effector is presented, which can decouple the translational and rotational motions about the axial direction and the axis of the end-effector. An active disturbance rejection controller and a variable impedance controller with particle swarm optimization and BP neural network are designed as the inner loop control and the outer loop control respectively. Moreover, a robotic active compliance constant force control method with the adaptive variable impedance is proposed to obtain the online adaptive optimization of impedance parameters and the dynamic adjustment of grinding force correction, and to realize the adaptive and active compliance constant force control for robotic grinding. The closed-loop stability of the proposed method is guaranteed by the Lyapunov stability theory. The effectiveness of the proposed method is verified by the co-simulation experiments on the virtual prototype platform of robotic grinding system and the physical experiment on the robotic experimental platform. The experimental results show that the proposed method can better realize the static and dynamic desired force tracking of the robotic grinding, reduce the grinding force fluctuation, force overshoot and the impact force of the grinding tool in the early stage of robotic grinding, improve the anti-disturbance stability, the constant force tracking performance and dynamic response ability of the robotic grinding force control system, and provide strong adaptability and robustness to handle the impact for the complicated and various working conditions of the robotic grinding.