We describe a technique to infer the kinematic parameters of the earthquake rupture process by the nonlinear inversion of near-source high-frequency seismic records. The model assumes that each point on the fault plane slips, when the rupture front passes, with a variable slip amplitude. For a given rupture model synthetic seismograms are computed by using the ray theory and a plane-layered velocity structure. The rupture velocity and the final slip are specified at a set of control points on the fault plane and the values at any point on the fault are then obtained by a bicubic interpolation. The final slip and rupture velocity at the fault-grid nodes are determined by searching for the minimum of a misfit function by using the Genetic Algorithm. The number of control points is progressively increased to move from a high- to low-wavelength description of final slip and rupture velocity on the fault plane. The optimal model parameter set is chosen according to the minimum of the corrected Akaike Information Criterion parameter. The uncertainty on the source parameters has been estimated through the analysis of cross-correlation of the misfit function in the neighborhood of the final, best-fit, rupture model. The method is applied to near-source, strong motion records of the 1989 Loma Prieta earthquake. We find that the most earthquake slip occurred in two regions located northwest and southeast of the hypocenter, consistent with previous models obtained using other data and techniques. Moreover, we find that the rupture propagated faster toward the southeast than in the northwest direction. The total duration of the rupture is found to be approximately 9 sec.