Abstract: In this paper,a synthesizing method,which can generate the artificial ground motion that not only matches the target response spectrum but envelopes the corresponding target power spectrum,is proposed.With respect to every controlling frequency of the response spectrum:firstly,by superimposing the incremental narrow-band time history,the response spectrum of artificial ground motion is made to equal to the target value;and then,with its response spectrum unchanged,the time history is further modulated in the time domain to make its average power spectrum envelope the target one.A numerical example illustrates that not only the ground motion time history generated by this method possesses high matching precision to the target response spectrum,but also its average power spectrum envelopes the target power spectrum.