In this paper, we propose a subspace identification method that involves a priori information of a system characterized in the frequency domain. We first transform the characteristics of the system over all frequency range into matrix inequalities that are linear in system matrices, by using the well-known Kalman-Yakubovich-Popov (KYP) lemma. To construct a model containing the specified frequency characteristics, we propose a subspace identification method under the matrix inequality constraints. Furthermore, the proposed method is extended to that involving with a priori information characterized only in a certain frequency range. Finally, we verify effectiveness of the proposed method in a numerical simulation.