In this paper, we combine the ideas of multilevel augmentation methods for solving integral equations and the shifted-inverse power method to develop a new multilevel augmentation method for solving eigen-problem of compact integral operators with smooth kernels. We first solve an eigen-problem in a suitable initial coarse level and then seek a more accurate approximation from solving a linear system on a finer mesh. Moreover, we need only to deal with a small linear system corresponding to the initial coarse level when we solve the linear system on a finer mesh. The method exhibits to be convenient for implementing adaptivity, and reduces the computational cost greatly and leads to the method faster. Numerical examples are presented to illustrate the theoretical estimates for the error of these methods.