In order to solve the problem that traditional control method is difficult to achieve high-precision grinding of complex surfaces, this paper designs the impedance control method of complex surface grinding robot based on nonsingular terminal sliding mode in Cartesian coordinate system. Firstly, according to the impedance model parameters of the system, the set grinding trajectory is transformed into the executable impedance trajectory at the end of the robot. Then a control method based on nonsingular terminal sliding mode is designed to track the impedance trajectory. For the chattering problem of sliding mode control, the exponential approach law is used to weaken it. The stability of the system is proved based on Lyapunov theory. Simulation and cylinder grinding experiment results show that the method can achieve convergence in a limited time and avoid the control singularity, and improve the robustness and accuracy of the control system.