A control design is proposed for a linear time-varying system which exhibits sustained but bounded state oscillations. The design is based on the gradient algorithm used in adaptive parameter identification. The resultant observer-based state feedback control guarantees exponential decay of the state oscillation given that the system is both uniformly controllable and uniformly observable. A unique feature of the proposed control design is that it requires neither information of time derivatives of the time-varying parameters, nor prediction of future information of the time-varying parameters.