It is necessary to estimate earthquake motion at the bedrock level from ground surface level records observed near the epicenter in order to elucidate the cause of damage to structures after a large-scale earthquake or to evaluate the design earthquake ground motion. The ground, however, shows nonlinear behavior from a relatively small strain level. For this reason, seismic records observed near the epicenter during a large-scale earthquake may be strongly affected by the nonlinearity of the ground. A frequency domain analysis method such as SHAKE is commonly used for estimating the earthquake motion at the bedrock level. In general, the frequency domain analysis method is used to calculate ground stiffness and damping by assuming that they are constant values throughout the earthquake. Therefore, it is impossible to consider changes in stiffness and damping during an earthquake. It follows that the amplitude of earthquake motion may be highly overestimated if the records used for estimation are strongly affected by the nonlinear behavior of the ground (e.g. seismic records with large amplitude or from positions on soft ground). Accordingly, this study proposes a method for estimating the bedrock ground motion to a high degree of accuracy from seismic observation records obtained on the ground surface. This method uses a common nonlinear optimization method for an inverse analysis, but the generation of physically meaningless short-period pulses is suppressed by using the perturbation waveform as the Ricker Wavelet. In the initial stage of convergence, the convergence properties are improved by setting the perturbation waveform to a large amplitude. In addition, the calculation time, which is an issue when estimating the bedrock ground motion using nonlinear time-history analysis, has been shortened by using the equivalent SDOF system of the ground in the initial stage of convergence calculation. The proposed method can estimate the bedrock ground motion with higher accuracy than the conventional method. In addition, it reduces the calculation time which is an issue in nonlinear time-history analysis. This method is expected to be used as a bedrock ground motion estimation method for investigating the causes of damage after large-scale earthquakes or evaluating the design earthquake ground motion.