The ground acceleration time histories generated using uniformly random phase spectrum are unable to model the nonstationarity in both the amplitudes and the frequency contents in a physically realistic way. Though the nonstationarity in amplitudes can be assigned easily using a deterministic envelope function, it is necessary to define a realistic phase spectrum to achieve the nonstationary frequency contents. Frequency nonstationarity may significantly influence the fatigue and nonlinear behavior of structures. This article proposes a method to define the Fourier phase spectrum of ground acceleration using empirically simulated equivalent group velocity dispersion curves. Empirical prediction relations are developed for the group velocity dispersion curves using a database of 378 horizontal components of accelerograms recorded from 67 different earthquakes at 61 sites in the western Himalayan region. The empirically predicted dispersion curves are shown to be in fairly good agreement with the actual dispersion curves for several real accelerograms with widely differing characteristics. The empirical dispersion curves are used to simulate the Fourier phase spectra for generation of synthetic accelerograms in this article. The synthetic accelerograms generated using Fourier amplitude spectra (FAS) of several real accelerograms are shown to have physically realistic nonstationary characteristics, as evidenced by comparisons between the peak ground accelerations, Husid plots, strong‐motion durations, and elastic pseudoacceleration response spectra of the real and the synthetic accelerograms. The proposed method can thus be considered to provide a useful practical approach for simulation of nonstationary design accelerograms in conjunction with the FAS defined from seismic hazard analysis or the seismological source model approach.