Perceiving speech while performing another task is a common challenge in everyday life. How the brain controls resource allocation during speech perception remains poorly understood. Using functional magnetic resonance imaging (fMRI), we investigated the effect of cognitive load on speech perception by examining brain responses of participants performing a phoneme discrimination task and a visual working memory task simultaneously. The visual task involved holding either a single meaningless image in working memory (low cognitive load) or four different images (high cognitive load). Performing the speech task under high load, compared to low load, resulted in decreased activity in pSTG/pMTG and increased activity in visual occipital cortex and two regions known to contribute to visual attention regulation—the superior parietal lobule (SPL) and the paracingulate and anterior cingulate gyrus (PaCG, ACG). Critically, activity in PaCG/ACG was correlated with performance in the visual task and with activity in pSTG/pMTG: Increased activity in PaCG/ACG was observed for individuals with poorer visual performance and with decreased activity in pSTG/pMTG. Moreover, activity in a pSTG/pMTG seed region showed psychophysiological interactions with areas of the PaCG/ACG, with stronger interaction in the high-load than the low-load condition. These findings show that the acoustic analysis of speech is affected by the demands of a concurrent visual task and that the PaCG/ACG plays a role in allocating cognitive resources to concurrent auditory and visual information.