High-precision and low-overshoot force control are important to guarantee the material removal rate and surface quality of robot grinding. However, traditional force control methods are subjected to positional disturbance, stiffness disturbance, contact process nonlinearity, and force-position coupling, leading to difficulties in robot constant force control. Therefore, how to achieve smooth, stable, and high-precision constant force control is an urgent problem. To address this problem, a dual PID adaptive variable impedance control is established (DPAVIC). Firstly, PD control is used to compensate for the force error, and PID is used to update the damping parameters to compensate for the disturbance. Secondly, a nonlinear tracking differentiator is used to smooth the desired force and reduce the contact force overshoot. Then, the stability, convergence, and effectiveness of the force control algorithm are verified via theoretical analysis, simulations, and experiments. The force tracking error and overshoot of a conventional impedance controller (CIC), adaptive variable impedance control (AVIC), and DPAVIC are analyzed. Finally, the algorithm is used in grinding experiments on a thin-walled workpiece. The force tracking error is controlled within ±0.2 N, and the surface roughness of the workpiece is improved to Ra 0.218 μm.