<p>Impedance control is widely used in robot-assisted curved surface polishing. However, during the polishing process, the performance of traditional impedance control is susceptible to environmental parameters, and system stability also depends on the position inner loop control. In order to overcome this drawback, a novel hybrid adaptive control strategy for robot-assisted curved surface polishing is proposed. The robot dynamics model is established, and Lyapunov method is utilized to examine the stability of proposed control strategy. Based on the impedance control, the terminal sliding mode control is adopted for the position inner loop. The RBF neural network is used to estimate the environmental parameters in real time and online to compensate the environmental parameter error of the polishing system. Simulation and experimental results demonstrate that the proposed control strategy can improve the trajectory tracking accuracy of polishing system effectively. The quality of polished surface has been significantly improved compared with traditional impedance control, and the arithmetical mean deviation of the roughness profile of the polished surface is 0.057 µm.</p>