To improve the computational efficiency of uncertainty analysis of the large-scale complex structures, a methodological method for interval uncertainty based on an improved free interface component mode synthesis method is proposed. Firstly, according to the characteristics of the system, the system is divided into substructures and the perturbation method is employed for the eigenvalue analysis of components with the interval non-deterministic characteristics. In order to reduce the mode truncation error, the residual flexibility matrix is deduced by constructing a set of weighted orthogonal modal vectors with low-order modes and system matrices. Different from the previous studies, this approach presented in this paper avoids calculating directly inverse of the stiffness matrix, which makes it easier to get the residual flexibility matrix. Then, the synthesis equations considering parameters perturbation can be obtained in terms of the interface compatibility conditions. Finally, a numerical example of a bridge in conjunction with a Monte Carlo simulation is given, the results show that the proposed method achieved a great efficiency improvement under the prerequisite of ensuring calculation accuracy.