Abstract: In this paper,a new type of narrow-band function is proposed for the artificial history simulation method based on narrow-band superposition,which aims to meet the needs of both fitting of the target response spectrum and envelop of the power spectral density.The new narrow-band function is based on the normal distribution function and trigonometric functions.Its band width can be controlled and it decays rapidly on both sides.While the target response spectrum is fitted by superimposing the new narrow-band time history,the power spectral density is enveloped by modifying the Fourier amplitude spectrum locally.The numerical example demonstrates that not only the artificial time history generated by this algorithm reaches high matching precision to the target response spectrum,but also the corresponding calculated power spectrum envelopes the target power spectrum.