One of the authors had previously proposed an adaptive nonstationary control (ANSC) method and described its applications for the positioning control of vibration systems. In that control method, the time-varying feedback gains were obtained by online computations of a time-varying Riccati equation taking the parameter variations of the controlled object into account. However, the previous paper discussed the state feedback control method. The improvement of this method to enable output feedback control is one of important issues for actual applications. Generally, the output feedback controller of the optimal control includes a Kalman filter as the observer. However, the use of the Kalman filter for the ANSC method implies a heavy computational load in actual implementations because the Kalman filter is designed by another time-varying Riccati equation. Therefore, this paper proposes a practical output feedback control method for ANSC that does not include Kalman filter. The proposed method corresponds to a two-degree-of-freedom control system; the system consists of an online simulator and a sliding mode controller. This structure enables us to reduce the computational load. The effectiveness of the method is verified theoretically as well as experimentally.