Industrial robots are finding their niche in the field of machining due to their advantages of high flexibility, good versatility, and low cost. However, limited by the low absolute positioning accuracy, there are still huge obstacles in high-precision machining processes such as grinding. Aiming at this problem, a compensation method combining analytical modeling for quantitative errors with spatial interpolation algorithm for random errors is proposed based on the full consideration of the source and characteristics of positioning errors. First, as for the quantitative errors, namely geometric parameter and compliance error in this paper, a kinematics-based error model is constructed taking the coupling effect of errors into consideration. Then avoiding the impact of random errors, the extended Kalman filtering (EKF) algorithm is adopted to identify the error parameters. Second, based on the similarity principle of spatial error, spatial interpolation algorithm is used to model the residual error caused by temperature, gear clearance, etc. Based on the spatial anisotropy characteristics of robot motion performance, an adaptive mesh division algorithm was proposed to balance the accuracy and efficiency of mesh division. Then, an inverse distance weighted interpolation algorithm considering the influence degree of different joints on the end position was established to improve the approximation accuracy of residual error. Finally, the rough-fine two-stage serial error compensation method was carried out. Experimental results show that the mean absolute positioning accuracy is improved from 1.165 mm to 0.106 mm, which demonstrates the effectiveness of the method in this paper.