The basolateral amygdala plays an important role in the acquisition and expression of both fear conditioning and fear extinction. To understand how a single structure could encode these "opposite" memories, we developed a biophysical network model of the lateral amygdala (LA) neurons during auditory fear conditioning and extinction. Membrane channel properties were selected in order to match waveforms and firing properties of pyramidal cells and interneurons in LA, from published in vitro studies. Hebbian plasticity was implemented in excitatory AMPA and inhibitory GABA_A receptor-mediated synapses to model learning. The occurrence of synaptic potentiation vs. depression was determined by intracellular calcium levels, according to the calcium control hypothesis. The model was able to replicate conditioning- and extinction-induced changes in tone responses of LA neurons in behaving rats. Our main finding is that LA activity during both acquisition and extinction can be controlled by a balance between pyramidal cell and interneuron activations. Extinction training depressed conditioned synapses and also potentiated local interneurons, thereby inhibiting the responses of pyramidal cells to auditory input. Both long-term depression and potentiation of inhibition were required to initiate and maintain extinction. The model provides insights into the sites of plasticity in conditioning and extinction, the mechanism of spontaneous recovery, and the role of amygdala NMDA receptors in extinction learning.