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To improve the efficiency of reliability calculations for vehicle-bridge systems, we present a surrogate modeling method based on a nonlinear autoregressive with exogenous input artificial neural network model and an important sample, which can forecast responses of dynamic systems, such as vehicle-bridge systems, subjected to stochastic excitations. We also propose a process to analyze the method. A quarter-vehicle model is used to verify the proposed method’s precision, and the nonlinear autoregressive with exogenous input artificial neural network model is used to predict responses of vertical vehicle-bridge systems. The results show that, compared to other training samples, the nonlinear autoregressive with exogenous input artificial neural network model has better prediction accuracy when the sample with the maximum response is considered as an important sample and is used to train the nonlinear autoregressive with exogenous input artificial neural network model, and it requires only two-time numerical simulation (or Monte Carlo simulation) at most, which is used in the training of the nonlinear autoregressive with exogenous input artificial neural network model.

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