Given that grinding robots are easily affected by internal and external disturbances when machining complex surfaces with high precision, in this study, an adaptive robust impedance control method combining a radial basis function neural network (RBFNN) and sliding mode control (SMC) is proposed. In a Cartesian coordinate system, we first use the universal approximation ability of the RBFNN to accurately identify and actively compensate for complex unknown disturbances in robot dynamics online. Then, an improved sliding mode impedance controller, which uses robust sliding mode control to effectively suppress the influence of RBFNN identification error and residual disturbance on trajectory tracking and ensure the accuracy of impedance control, is implemented. This approach improves the control performance and overcomes the inherent chattering phenomenon of the traditional sliding mode.