By using the theory of multi-body system and Denavit-Hartenberg homogeneous coordinate transformation,the geometric error and thermal error of face gear NC grinding machine is analyzed.According to the principle of face gear meshing and production mechanism of the grinding error,the mathematic model of comprehensive error contains geometric error and thermal error of the face gear NC grinding machine tool is established.Based on the little error assumption and using Matlab software,the error expression which contains six degrees of freedom is got,additionally,the relationship between the six degrees of freedom and six errors which produced by the grinding wheel spindle movement is analyzed and validated.The basis for improve the machining accuracy of gear and error modeling is provided.