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In this paper, a multi-branch back propagation neural network (BPNN) is adopted to predict the nonlinear seismic responses of an eccentric three-story reinforced concrete building. First of all, the network is trained in batch by the vibration table test data of the structure with the maximum acceleration of ground motion in 0.4g. Then, the trained network is used for structural responses prediction. The nonlinear structural acceleration responses of the each story are evaluated by the trained network for the maximum acceleration of ground motion in different amplitudes. Compared with the experimental results, it turns out that the trained network can accurately predict structural future dynamic responses.