The rapid computation of random eigenvalue problems of uncertain structures is the key point in structural dynamics, and it is prerequisite to the efficient dynamic analysis and optimal design of structures. In this paper, by combining finite element-transfer matrix method (FE-TMM) with perturbation method, a new method named as perturbation FE-TMM is presented for random eigenvalue problems of uncertain structures. By using the proposed method, the rapid computation of random eigenvalue problems of uncertain structures with complicated shapes and boundaries can be achieved, and the repeated eignvalues and characteristic vectors can be solved conveniently. Compared with stochastic finite element method, this method has the low memory requirement, high computational efficiency and high computational stability. It has more advantages for dynamic design of uncertain structures. Formulations as well as some numerical examples are given to validate the method.