Abstract: In this paper,a method of superposing narrow-band time history in time domain is proposed,which can be utilized to enhance the fitting precisions of design ground shaking time history to multi-damping specified single-damping target response spectrum;and then by superposing narrowband time histories in time domain,the initial acceleration time history is further modulated,to improve its fitting precision to the multi-damping target response spectra.The numerical examples demonstrated that the design ground motions generated by the proposed method possess very high fitting precisions to the multi-damping target spectra.