In this study, an artificial neural network (ANN)-based surrogate model is proposed to evaluate the system-level seismic risk of bridge transportation networks efficiently. To estimate the performance of a network, total system travel time (TSTT) was introduced as a performance index, and an ANN-based surrogate model was incorporated to evaluate a high-dimensional network with probabilistic seismic hazard analysis (PSHA) efficiently. To generate training data, the damage states of bridge components were considered as the input training data, and TSTT was selected as output data. An actual bridge transportation network in South Korea was considered as the target network, and the entire network map was reconstructed based on geographic information system data to demonstrate the proposed method. For numerical analysis, the training data were generated based on epicenter location history. By using the surrogate model, the network performance was estimated for various earthquake magnitudes at the trained epicenter with significantly-reduced computational time cost. In addition, 20 historical epicenters were adopted to confirm the robustness of the epicenter. Therefore, it was concluded that the proposed ANN-based surrogate model could be used as an alternative for efficient system-level seismic risk assessment of high-dimensional bridge transportation networks.