A computer model is presented of a neural circuit that replicates amplitude-modulation (AM) sensitivity of cells in the central nucleus of the inferior colliculus (ICC). The ICC cell is modeled as a point neuron whose input consists of spike trains from a number of simulated ventral cochlear nucleus (VCN) chopper cells. Input to the VCN chopper cells is provided by simulated spike trains from a model of the auditory periphery [Hewitt et al., J. Acoust. Soc. Am. 91, 2096-2109 (1992)]. The performance of the model at the output of the auditory nerve, the cochlear nucleus and ICC simulations in response to amplitude-modulated stimuli is described. The results are presented in terms of both temporal and rate modulation transfer functions (MTFs) and compared with data from physiological studies in the literature. Qualitative matches were obtained to the following main empirical findings: (a) Auditory nerve temporal-MTFs are low pass, (b) VCN chopper temporal-MTFs are low pass at low signal levels and bandpass at moderate and high signal levels, (c) ICC unit temporal-MTFs are low pass at low signal levels and broadly tuned bandpass at moderate and high signal levels, and (d) ICC unit rate-MTFs are sharply tuned bandpass at low and moderate signal levels and flat at high levels. VCN and ICC units preferentially sensitive to different rates of modulation are presented. The model supports the hypothesis that cells in the ICC decode temporal information into a rate code [Langner and Schreiner, J. Neurophysiol. 60, 1799-1822 (1988)], and provides a candidate wiring diagram of how this may be achieved.