In order to grind the drag reducing structured surface with dimples,based on the kinematic relationship of grinding and the point set topology theory,a method for topological grinding of the structured surface was proposed.The topological characteristics of structured surface with dimples were analyzed,the topological mapping matrix between the structured surface and the structured grinding wheel was established according to the creation mechanism of the structured surface,and the abrasive cluster grinding wheel was designed.The topological grinding motion trajectory model was established,and the grinding process was simulated by MatLab to analyze the influence of parameters such as speed ratio and grinding depth on the surface topography.The simulation and analysis results show that the topological grinding method and the reasonable selection of parameters such as speed ratio and grinding depth can grind a structured drag reducing surface with a specific shape on the surface of the workpiece.As the speed ratio increases,the length of the dimples and the lengthwise arrangement period increase.As the grinding depth increases,the length and width of the dimples increase,and the arrangement period remains unchanged.