This study developed a nonlinear behavior prediction model for elasto-plastic steel coil dampers (SCDs) using artificial neural networks (ANN). To train the ANN, first, the input and output data of the behavior of the elasto-plastic SCD was prepared. This study utilized the design parameters and load–displacement curves of the SCD to train the ANN. The elasto-plastic load–displacement curve of the SCD was obtained from simulation results using an ANSYS workbench. The design parameters (wire diameter, internal diameter, number of active windings, yield strength) of the SCD were defined as the input patterns, while the yield deformation, first stiffness, and second stiffness were output patterns. During learning of the neural network model, 60 datasets of the SCD were used as the learning pattern, and the remaining 21 were used to verify the model. Although this study used a small number of learning patterns, the ANN predicted accurate results for yield displacement, first stiffness, and second stiffness. In this study, the ANN was found to perform very well, predicting the nonlinear response of the SCD, compared with the values obtained from a finite element analysis program.