To address the problem that the number of geometric errors were inconsistent and incompleteness which needed to be measured for the rotary axis of four axis horizontal boring machine, an analyzing methodology of PIGEs formation mechanism based on the shape generation function and a method of the completeness measuring, identifying geometric errors of the rotary axis were proposed for a four axis horizontal boring machine. Firstly, the generation function of PIGEs of horizontal boring machines was constructed based on the shape generation mechanism, and the minimum number of position-independent geometric error (PIGEs) that the rotary axis can be adjusted through error compensation was determined. Secondly, the completeness function model was established consisted of four terms PIGEs, six terms position-dependent geometric error (PDGEs), six terms setup error (SEs) and DBB measurement track radius length of the rotary axis of horizontal boring machine, the Viviani curve measurement track based on DBB was designed based four-axis synchronized motion, and the NURBS characterization of six item PDGEs, identification methods of PIGEs, and SEs of the rotary axis were constructed. Finally, the comparative experiment by error compensating was carried out. The results showed that the error compensation using the geometric error completeness measurement and identification results included four terms PIGEs, six terms PDGEs, and six terms SEs can improve the measurement accuracy of circular trajectory by 40.69% compared with that of compensate six PDGEs simply.