An elevated station has a shed above a viaduct. Generally, sheds have extremely smaller mass than viaducts. In a mass-variable 2-DOF structure like elevated stations, large response acceleration tends to be raised on the upper story when seismic motions are inputted. In this paper, as a method of reducing the acceleration, we propose applying an inertial mass damper to its upper story. Through shaking table tests and analyses, it is shown that the large acceleration on the upper story can be reduced by the method.