Abstract: In this paper, the grinding accuracy of a CNC external circular compound grinding machine was analyzed. According to the structure characteristics of the grinding machine, the analysis of turret type multi-spindle grinding wheel frame was added. In the establishment of the precision grinding equation, the non-verticality error of the turret in the vertical direction was considered.Firstly, based on the multi-body system theory, the topological structure of the compound grinding machine is established, the position equation of grinding point of the grinding wheel in the grinding wheel coordinate system and the workpiece coordinate system is established, the coordinate system of each part of the grinding machine is determined, the transformation matrix is obtained, and the precision grinding equation is obtained according to the equality of the two branch equations.The equation is solved by MATLAB, which provides conditions for the subsequent error compensation.