Due to the geometric error nfluence,the existing research mainly considers the geometric error compensation of end-mechanism or key moving-axis,lacks successive compensation of moving-axis-geometric-error.In order to avoid error accumulation effect caused by geometric error chain of on-machine inspection mechanism and effectively improve on-machine inspection accuracy,according to the on-machine inspection principle of the independently developed horizontal gear grinder,based on the multi-rigid body system kinematics and homogeneous coordinate transformation theory,the geometric error chain model of on-machine inspection mechanism is established. After the moving-axis-gcometic-errors of geometric error chain are identified and compensated step by step,the standard sample gear inspections of the gear grinder were carried out. Results show that before and afte error compensation,the tooth lead accuracies are both at level 4; afer erro compensation,the tooth profile accuracy is improved by 4 grades and is at level 4,which is consistent with the result of Gleaso inspections.The results verify the correctness of the model,which is expected to be used in high-precision on-machine inspection system of gear grinder.