In foreign-accented speech, pronunciation typically deviates from the canonical form to some degree. For native listeners, it has been shown that word recognition is more difficult for strongly-accented words than for less strongly-accented words. Furthermore recognition of strongly-accented words becomes easier with additional exposure to the foreign accent. In this paper, listeners’ behaviour was simulated with Fine-tracker, a computational model of word recognition that uses real speech as input. The simulations showed that, in line with human listeners, 1) Fine-Tracker’s recognition outcome is modulated by the degree of accentedness and 2) it improves slightly after brief exposure with the accent. On the level of individual words, however, Fine-tracker failed to correctly simulate listeners’ behaviour, possibly due to differences in overall familiarity with the chosen accent (German-accented Dutch) between human listeners and Fine-Tracker.