A new indirect approach for designing low-order linear-phase IIR filters is presented in this paper. Given an FIR filter, we utilize a new Krylov subspace projection method, called the rational Arnoldi method with adaptive orders, to synthesize an approximated IIR filter with small orders. The synthesized IIR filter can truly reflect essential dynamical features of the original FIR filter and indeed satisfies the design specifications. Also, from simulation results, it can be observed that the linear-phase property in the passband is stilled retained. This indirect approach is accomplished using the state-space realization of FIR filters, multi-point Pade approximations, the Arnoldi algorithm, and an intelligent scheme to select expansion points in the frequency domain. Such methods are quite efficient in terms of computational complexity. Fundamental developments of the proposed method will be discussed in details. Numerical results will demonstrate the accuracy and the efficiency of this two-step indirect method.