It is well-known that preprocessing of the measured input-output data is very important to obtain accurate parameter estimates by system identification methods. This paper treats LTI (linear time-invariant) systems with integrators that appear in various engineering fields, for example, a physical system with rigid body motion and DC servo motors. However, it is known that it is difficult to identify the systems with integrators because they are unstable and astatic system. The purpose of this paper is to propose an appropriate preprocessing method and an identification procedure for the systems with integrators. First, preprocessing of input-output data for such systems is proposed, which removes low-frequency disturbances. Second, a new identification procedure for such systems is proposed, which applies an integrator on input data. Finally, effectiveness of the proposed methods is examined through numerical examples.