A procedure for building a kinematic source model is proposed in this article for the synthesis of broadband ground motion based on the frequency–wavenumber Green’s function. The spatial distribution of slip on the rupture plane is generated by combining asperity slip with random slip. A set of scaling laws recently updated for the global and local parameters of seismic sources is adopted. To characterize the temporal evolution of slip on the rupture plane, different rupture velocities, and rise times are first generated by considering the correlation with slip, and a source time function obtained by rupture dynamics is selected for each subsource. Then, the entire rupture process is set as the object to jointly determine the rise time and rupture velocity for a given slip distribution under the selection criterion that the entire rupture process should radiate the closest seismic energy to the expected energy. To reduce uncertainty, 30 spatiotemporal rupture processes for an earthquake scenario are realized to select a mean source model. To demonstrate the feasibility of the proposed source modeling approach, two California earthquakes, the Whittier Narrows earthquake and the Loma Prieta earthquake, are chosen as case studies. The performance of the obtained source models shows that our modeling approach is advantageous for estimating the size of the rupture plane, emphasizing the effect of asperity, and considering the correlation between temporal rupture parameters and slip. The bias values between the observed and synthetic pseudospectral accelerations are relatively small compared to those for the methods on the Southern California Earthquake Center broadband platform. The synthetics are further compared with the estimates from regional ground‐motion prediction equations for four scenario earthquakes with moment magnitudes of 6.0, 6.5, 7.0, and 7.5. Finally, the sensitivity of the synthetic motion to various rupture parameters is analyzed.