The temporal relationship between auditory and visual cues is a fundamental feature in the determination of whether these signals will be integrated. The window of perceived simultaneity (TBW) is a construct that describes the epoch of time during which asynchronous auditory and visual stimuli are likely to be perceptually bound. Recently, a number of studies have demonstrated the capacity for perceptual training to enhance temporal acuity for audiovisual stimuli (i.e., narrow the TBW). These studies, however, have only examined multisensory perceptual learning that develops in response to feedback that is provided when making judgments on simple, low-level audiovisual stimuli (i.e., flashes and beeps). Here we sought to determine if perceptual training was capable of altering temporal acuity for audiovisual speech. Furthermore, we also explored whether perceptual training with simple or complex audiovisual stimuli generalized across levels of stimulus complexity. Using a simultaneity judgment (SJ) task, we measured individuals' temporal acuity (as estimated by the TBW) prior to, immediately following, and one week after four consecutive days of perceptual training. We report that temporal acuity for audiovisual speech stimuli is enhanced following perceptual training using speech stimuli. Additionally, we find that changes in temporal acuity following perceptual training do not generalize across the levels of stimulus complexity in this study. Overall, the results suggest that perceptual training is capable of enhancing temporal acuity for audiovisual speech in adults, and that the dynamics of the changes in temporal acuity following perceptual training differ between simple audiovisual stimuli and more complex audiovisual speech stimuli.