The problem of reduced order modeling for linear fractional-order systems is investigated based on the unsymmetric Lanczos algorithm, and a reduced order modeling method is proposed to retain a certain number of fractional- order moments of transfer functions. According to the operation principle of Caputo derivative, the computing method of fractional-order moment of the linear fractional-order system is given. By using the unsymmetric Lanczos algorithm, the corresponding unsymmetric tridiagonal matrix is constructed. Based on the properties of the unsymmetric tridiagonal matrix, it is proved that the reduced order systems and the original systems have a certain number of fractional-order moments. Besides, the error estimation with respect to the the transfer functions between the reduced order system and the original system is given, providing the theoretical basis for choosing the order of the reduced order system. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.