The seismic response analysis of local complex sites with nonlinear characteristics has been the key problem to solve in prediction of seismic motion. Frequency domain equivalent linearization, widely used in the seismic response analysis of one-dimensional stratified sites, is extended to time domain and two-dimensional problems. A time-domain explicit finite element method can be used to consider nonlinear characteristics and it is suitable for seismic response analysis of complex engineering sites. In this method, the inner domain of the method is mainly used to realize the low-order finite element scheme of the explicit algorithm. The boundary of the artificial boundary is simulated by the boundary of the transmission boundary. The maximum tangent strain in the one-dimensional model is replaced by the maximum tangent strain in the plane strain state, and the equivalent shear strain is obtained according to the tangent strain of the whole time process. Each time the whole solution is solved by the time domain center difference, and the nonlinear characteristic analysis is done by iteration. In order to verify this method, two typical site models of horizontal stratified and two-dimensional basins are selected for simulation analysis. The results are compared with solutions of the traditional one-dimensional equivalent linearization model and the two-dimensional differential nonlinear calculation. The results show that the solution is in good agreement with the reference solution, and prove the reliability of the method. This method is used to simulate the surface vibration of the US Turkey Flat test site. The results are compared with one-dimensional equivalent linearization model and the measured record. The reliability of the method and the difference with the existing analysis model are discussed, and the influence of the nonlinear characteristics on the seismic motion is illustrated.