In this study, we investigated one type of auditory perceptual grouping phenomena—the auditory continuity illusion (also called temporal induction). We employed a previously developed, neurobiologically realistic, large-scale neural network model of the auditory processing pathway in the cortex, ranging from the primary auditory cortex to the prefrontal cortex, and simulated temporal induction without changing any model parameters. The model processes tonal contour stimuli, composed of combinations of upward and downward FM sweeps and tones, in a delayed match-to-sample task. The local electrical activities of the neuronal units of the model simulated accurately the experimentally observed electrophysiological data, where available, and the model's simulated BOLD-fMRI data were quantitatively matched with experimental fMRI data. In the present simulations, intact stimuli were matched with fragmented versions (i.e., with inserted silent gaps). The ability of the model to match fragmented stimuli declined as the duration of the gaps increased. However, when simulated broadband noise was inserted into these gaps, the matching response was restored, indicating that a continuous stimulus was perceived. The electrical activities of the neuronal units of the model agreed with electrophysiological data, and the behavioral activity of the model matched human behavioral data. In the model, the predominant mechanism implementing temporal induction is the divergence of the feedforward connections along the auditory processing pathway in the temporal cortex. These simulation results not only attest to the robustness of the model, but further predict the primary role of the anatomical connectivity of the auditory processing areas in mediating the continuity illusion.