Reinforcement learning based on rewarding or aversive stimuli is critical to understanding the adaptation of cognitive systems. One of the most basic and well-studied forms of reinforcement learning in mammals is found in fear conditioning. We present a biologically plausible spiking neuron model of mammalian fear conditioning and show that the model is capable of reproducing the results of four well known fear conditioning experiments (conditioning, second-order conditioning, blocking, and context-dependent extinction and renewal). The model contains approximately 2000 spiking neurons which make up various populations of primarily the amygdala, periaqueductal gray, and hippocampus. The connectivity and organization of these populations follows what is known about the fear conditioning circuit in mammalian brains. Input to the model is made up of populations representing sensory stimuli, contextual information, and electric shock, while the output is a population representing an autonomic fear response: freezing. Using a novel learning rule for spiking neurons, associations are learned between cues, contexts, and the aversive shock, reproducing the behaviors seen in rats during fear conditioning experiments.