In this paper, a synthesizing method based on the Hilbert transform is proposed to generate artificial earthquake ground‐motion samples, the nonstationary features of which are similar to those of given natural seismic recordings. With this aim in mind, the given natural seismogram, assumed to be a sample of some underlying random process, is first processed by the Hilbert transform to obtain its instantaneous amplitude and instantaneous phase functions. The instantaneous amplitude function is treated as an invariant variable for which the value will be preserved into the synthetic samples, whereas the instantaneous phase function is treated stochastically to address the randomness of the underlying ground‐motion process. By establishing the stochastic model for the instantaneous phase function, the underlying ground‐motion random process can be determined, and a series of its samples can be generated numerically. Synthetic examples demonstrate that the ground‐motion samples generated by the proposed method can maintain the general time‐variant features of original natural ground motions, and the method has application potential either in the engineering practice or in earthquake engineering research.