Abstract: When using numerical methods to synthesize ground motions, in addition to fitting the response spectrum, the fitting of peak displacements and the simulation of the non-stationary characteristics of natural ground motions also have important significance and engineering application prospects. Based on the wavelet function fitting method, this paper proposes a ground motion acceleration time history that can synthesize the target response spectrum and peak displacement at the same time. Numerical calculation examples show that this method has a faster rate of convergence, and can achieve a higher precision fitting of the target response spectrum and target peak displacement through less iterative calculations. Moreover, compared with other existing methods, the ground motion synthesized by this method can retain the non-stationary characteristics of natural ground motion, due to the local characteristics of wavelet function in time domain.