Many past studies of sound localization explored the precedence effect (PE), in which a pair of brief, temporally close sounds from different directions is perceived as coming from a location near that of the first-arriving sound. Here, a computational model of low-frequency inferior colliculus (IC) neurons accounts for both physiological and psychophysical responses to PE click stimuli. In the model, IC neurons have physiologically plausible inputs, receiving excitation from the ipsilateral medial superior olive (MSO) and long-lasting inhibition from both ipsilateral and contralateral MSOs, relayed through the dorsal nucleus of the lateral lemniscus. In this model, physiological suppression of the lagging response depends on the inter-stimulus delay (ISD) between the lead and lag as well as their relative locations. Psychophysical predictions are generated from a population of model neurons. At all ISDs, predicted lead localization is good. At short ISDs, the estimated location of the lag is near that of the lead, consistent with subjects perceiving both lead and lag from the lead location. As ISD increases, the estimated lag location moves closer to the true lag location, consistent with listeners' perception of two sounds from separate locations. Together, these simulations suggest that location-dependent suppression in IC neurons can explain the behavioral phenomenon known as the precedence effect.