Humans are able to follow a speaker even in challenging acoustic conditions. The perceptual mechanisms underlying this ability remain unclear. A computational model of attentive voice tracking, consisting of four computational blocks: (1) sparse periodicity-based auditory features (sPAF) extraction, (2) foreground-background segregation, (3) state estimation, and (4) top-down knowledge, is presented. The model connects the theories about auditory glimpses, foreground-background segregation, and Bayesian inference. It is implemented with the sPAF, sequential Monte Carlo sampling, and probabilistic voice models. The model is evaluated by comparing it with the human data obtained in the study by Woods and McDermott [Curr. Biol. 25(17), 2238–2246 (2015)], which measured the ability to track one of two competing voices with time-varying parameters [fundamental frequency (F0) and formants (F1,F2)]. Three model versions were tested, which differ in the type of information used for the segregation: version (a) uses the oracle F0, version (b) uses the estimated F0, and version (c) uses the spectral shape derived from the estimated F0 and oracle F1 and F2. Version (a) simulates the optimal human performance in conditions with the largest separation between the voices, version (b) simulates the conditions in which the separation in not sufficient to follow the voices, and version (c) is closest to the human performance for moderate voice separation.