Extensive fear extinction research is guided by the view that there are structures in the brain that develop inhibitory control over the expression of conditioned fear memories. While the medial prefrontal cortex has recently captured attention as the locus of plasticity essential for extinction of conditioned fear, the auditory cortex is another plausible cortical area involved in extinction learning since it is considered a sufficient conditioned stimulus (CS) pathway in tone fear conditioning. We examined the role of auditory cortex in extinction of auditory-based fear memories with a standard tone-on conditioning, wherein a tone CS predicted a footshock unconditioned stimulus (US), or a novel tone-off conditioning, in which the tone was continually present and the offset of the tone was the CS predicting the US. Rats with bilateral auditory cortex lesions were trained in either paradigm and subsequently trained in extinction to the CS. Auditory cortex lesions had no effect on acquisition but impaired extinction to both CSs. These findings indicate that the auditory cortex contributes to extinction of wide-ranging auditory fear memories, as evidenced by deficits in both tone-on CS and tone-off CS extinction training.