A design basis ground motion is usually defined to be compatible with a given response spectrum which is a useful measure of linear dynamic response of a structure. It has been known that the variance of maximum displacement responses to artificial ground motions in elasto-plasric region is quite large, although every artificial ground motion fits the same design response spectrum. Recently, a new synthesis method was proposed by Masuda, et al. that can generate artificial earthquake ground motions compatible with given time-frequency characteristic as well as a given response spectrum. In this paper, a group of artificial earthquake ground motions are generated, and elasto-plastic response analyses are carried out to examine variance of structural responses in elasto-plastic region. It is revealed that the variance of the structural responses to the earthquake ground motions generated by Masuda's method is less than that to the seismic ground motions by the conventional design method. And it is suggested that the given time-frequency characteristic has an effect on the variance of maximum responses.