Spindle is a typical multi-bearing rotor system, it is difficult to analyze its accuracy due to the extensive parallel connection in its structure and the mutual coupling of bearing and component errors. To address this problem, this study introduces a novel approach for analyzing the rotation accuracy of aviation manufacturing spindles. Firstly, the small displacement torsor theory and the skin model method were used to model the form and location tolerance and rotation trajectory of the bearings to construct a full tolerance model of the components. Secondly, the full parallel connection in the spindle was analyzed, and a method for analyzing the rotation accuracy of the spindle based on the optimization method solving the error propagation of components was proposed. Finally, the tolerance analysis and sensitivity calculation of a certain type of grinding spindle are carried out using the proposed method, and the results show that the method can effectively analyze the rotation accuracy of the spindle and the pass rate of accuracy increases from 74.3% to 88.2% through improved tolerance design, demonstrating an effectively improved tolerance design level of the spindle.