In this paper, the volumetric error decoupling and compensation method of CNC worm wheel grinding machine is studied. Firstly, based on the multi-body system theory and homogeneous coordinate transformation, the transformation matrix between machine tools is established, and the machine tool space error model caused by geometric error elements is derived. Then, the machine space error is step-by-step deupled based on the posture matrix and position matrix respectively. Finally, an example calculation of the step-by-step decoupling compensation method is carried out by specific numerical calculations, and the correctness and effectiveness of the spatial error decoupling compensation theory are verified.