In this letter, a synthesis method of the stabilized observers with a function of estimating unmeasurable inputs (OFE) to second-order lag systems is proposed. The basic idea is to synthesize the compensator gain of OFE such that one pole of OFE can be freely given while another can be chosen from the stable area. Usefulness of the proposed method is illustrated by a numerical example with the stabilization of the OFE and the estimation performance of disturbances.