Empirical research has shown that the amygdala, hippocampus, and ventromedial prefrontal cortex (vmPFC) are involved in fear conditioning. However, the functional contribution of each brain area and the nature of their interactions are not clearly understood. Here, we extend existing neural network models of the functional roles of the hippocampus in classical conditioning to include interactions with the amygdala and prefrontal cortex. We apply the model to fear conditioning, in which animals learn physiological (e.g. heart rate) and behavioral (e.g. freezing) responses to stimuli that have been paired with a highly aversive event (e.g. electrical shock). The key feature of our model is that learning of these conditioned responses in the central nucleus of the amygdala is modulated by two separate processes, one from basolateral amygdala and signaling a positive prediction error, and one from the vmPFC, via the intercalated cells of the amygdala, and signaling a negative prediction error. In addition, we propose that hippocampal input to both vmPFC and basolateral amygdala is essential for contextual modulation of fear acquisition and extinction. The model is sufficient to account for a body of data from various animal fear conditioning paradigms, including acquisition, extinction, reacquisition, and context specificity effects. Consistent with studies on lesioned animals, our model shows that damage to the vmPFC impairs extinction, while damage to the hippocampus impairs extinction in a different context (e.g., a different conditioning chamber from that used in initial training in animal experiments). We also discuss model limitations and predictions, including the effects of number of training trials on fear conditioning.