Vibration monitoring by virtual sensing methods has been well developed for linear time-invariant structures with limited sensors. However, few methods are proposed for Time-Varying (TV) structures which are inevitable in aerospace engineering. The core of vibration monitoring for TV structures is to describe the TV structural dynamic characteristics with accuracy and effi-ciency. This paper propose a new method using the Long Short-Term Memory (LSTM) networks for Continuously Variable Configuration Structures (CVCSs), which is an important subclass of TV structures. The configuration parameters are used to represent the time-varying dynamic character-istics by thefreezing"method. The relationship between TV dynamic characteristics and vibration responses is established by LSTM, and can be generalized to estimate the responses with unknown TV processes benefiting from the time translation invariance of LSTM. A numerical example and a liquid-filled pipe experiment are used to test the performance of the proposed method. The results demonstrate that the proposed method can accurately estimate the unmeasured responses for CVCSs to reveal the actual characteristics in time-domain and modal-domain. Besides, the average one-step estimation time of responses is less than the sampling interval. Thus, the proposed method is promising to on-line estimate the important responses of TV structures.