In response to the impact of curvature radius on the precision of robot abrasive belt polishing in the polishing process of complex curved parts, an experimental study on robot abrasive belt polishing based on multi curvature radius nickel based high-temperature alloy was carried out. The main focus was on exploring the machining performance of test pieces with different curvature radii, setting corresponding sand belt particle size and polishing process parameters for abrasive belt polishing of nickel based high-temperature alloy test pieces with different curvature radii, collecting the material removal depth of the test piece and analyzing the experimental results. The experimental results show that the variation of curvature radius has a certain impact on the depth of material removal. As the curvature radius changes from large to small, the depth of material removal also increases, indicating a negative correlation between the depth of material removal and the curvature radius. Based on a multiple nonlinear regression model, prediction model for the depth of material removal in robot abrasive grinding and polishing is proposed on the abrasive belt particle size, feed rate, contact force and workpiece curvature radius. The average prediction error of the prediction model is 1.45 μm, an accuracy rate is 91.04%, and a prediction error range is – 5.34–4.57 μm. The significance test of the prediction model indicates that the prediction model can provide important theoretical support for the early process parameter design of actual robot abrasive belt grinding and polishing processing.