The article provides a novel method to control the amount of unbalance propagation in precise cylindrical components assembly, which takes the machining error, the measurement error, and the assembly error into account. The coefficient and the correction factor matrices of mass eccentric deviations are defined to analyze the amount of unbalance propagation by building the connective assembly model. The influence of the machining error, the measurement error, and the assembly error on the mass center is analyzed in the assembly. The cumulative mass eccentric deviation can be reduced stage by stage in the assembly, and the amount of unbalance of final assembly can be minimized by controlling the assembly angle of each component. The effectiveness of the proposed method is verified by the assembly of the real aero-engine using the optimal assembly strategy. Compared to the worst assembly strategy, the values of the amount of unbalance using the optimal assembly strategy are reduced by 20%, 76%, and 79% for two, three, and four components assembly, respectively. Besides, the reasonable tolerance design area for each component is obtained with the proposed method for the real aero-engine assembly with four components. The proposed method can improve the assembly accuracy of cylindrical components and can be used for assembly guidance and tolerance design, especially for the assembly of multistage precise cylindrical components.