Faced with the difficulty of analyzing structural nonlinear seismic response, this study focuses on the reinforced concrete frame structure and designs a frame that meets the specifications. Artificial synthetic seismic records and natural seismic records were selected, and the acceleration response of the first story of the structure was used as the output sample for the study. On the basis of a nonlinear autoregressive moving average model with external inputs, a neural network model was constructed and nonlinear seismic response simulation analysis was conducted. These results confirm that the research method has good predictive performance and can effectively predict structural nonlinear seismic response. Under the action of artificial earthquake records, there is a small difference between them and the acceleration time history curve and acceleration response peak obtained from time history analysis. Under the action of artificial seismic record ACC12, when the time is 25 s, the calculation results of time history analysis and research methods are 1.715 m/s2 and 1.403 m/s2, respectively, with the former being 0.312 m/s2 smaller than the latter. In natural earthquake records, with a characteristic period of 0.30 s, under the action of natural earthquake record USA00668, the relative energy of time history analysis is 4.997 m2/s when the time is 30 s, which is 0.938 m2/s higher than the research method. The research method can accurately analyze the nonlinear seismic response of the results.