Beam-column connections exhibit complex behavior and often suffer damage during earthquakes. Beam-column connection failures in steel structures during the two major earthquakes of Northridge, 1994, and Hyogo-ken Nanbu, 1995 have underscored the importance of reliable modeling of these connections; models that include their main governing response modes under hysteretic loading. Many different modeling approaches have been applied to steel (and composite) beam-to-column connections over the past 3 decades. In this paper, a new neural network based inelastic hysteretic model for steel beam-column connections is proposed. The neural network (NN) model employs a component-based approach whereby the main components of the connection, and the interaction between them, are simulated separately. A welded beam-column connection (pre-Northridge type) is selected to demonstrate the proposed method. A self-learning simulation algorithm based on an auto-progressive methodology is employed so that the model can reproduce realistic hysteretic moment-rotational behavior. The proposed methodology is general and it has applications beyond the steel beam-column connection. The proposed framework can also be applied to other types of connections and many other structural systems.