This paper presents an identification algorithm of the dynamic characteristics, such as the natural frequency and the damping factor, of a structure deteriorating under natural environment. In this method, both an acceleration record x(t) of a seismic ground motion at the location of the structure and the structural displacement y(t) due to the ground motion are required. In addition, the respective non-stationary spectrum of x(t) and y(t) and the modulating function of x(t) found from evolutionary spectrum analysis are required. The applicability of the proposed method was shown according to the numerical analysis to a one-degree of freedom system. In the case of a multi-degree of freedom system, the dynamic properties of each mode can be obtained by making use of the modal analysis method. However, the identification of the natural modes of the system will be an important task in the future.