A composite source model is presented for convolution with synthetic Green's functions, in order to synthesize strong ground motions due to a complex rupture process of a large earthquake. Subevents with a power-law distribution of sizes are located randomly on the fault. Each subevent radiates a displacement pulse with the shape of a Brune's pulse in the far field, at a time determined by a constant rupture velocity propagating from the hypocenter. Thus, all the input parameters have a physical basis. We simulate strong ground motions for event--station pairs that correspond to records obtained in Mexico by the Guerrero accelerograph network. The synthetic accelerations, velocities, and displacements have realistic amplitudes, durations, and Fourier spectra.