People are much better at understanding speech when it is spoken by a familiar talker—such as a friend or partner—than when the interlocutor is unfamiliar. This provides an opportunity to examine the substrates of intelligibility and familiarity, independent of acoustics. Is the familiarity effect evident as early as primary auditory cortex, or only at later processing stages? Here, we presented sentences spoken by naturally familiar talkers (the participant’s friend or partner) and unfamiliar talkers (the friends or partners of other participants). We compared multivariate activity in speech-sensitive regions of cortex between conditions in which target sentences were presented alone and conditions in which the same target sentences were presented at the same time as a competing sentence. Using representational similarity analysis (RSA), we demonstrate that the pattern of activity evoked by a spoken sentence is less degraded by the presence of a competing sentence when it is spoken by a friend or partner than by someone unfamiliar; the results cannot be explained by acoustic differences since familiar and unfamiliar talkers were nearly identical across the group. This familiar-voice advantage is most prominent in nonprimary auditory cortical areas, along the posterior superior and middle temporal gyri. Across participants, the magnitude of the familiar-unfamiliar RSA difference correlates with the familiar-voice benefit to intelligibility. Overall, our results demonstrate that experience-driven improvements in intelligibility are associated with enhanced patterns of neural activity in nonprimary auditory cortical areas.Significance statementSpeech is a complex signal, and we do not yet fully understand how the content of a spoken sentence is encoded in cortex. Here, we used a novel approach based on analysing multivariate activity: we compared activity evoked by highly intelligible sentences presented alone and by the same sentences presented with a competing masker. The distributed pattern of activity in speech-sensitive regions of the brain was more similar between the alone and masker conditions when the target sentence was spoken by someone familiar—the participant’s friend or partner—than someone unfamiliar. This metric correlated with the intelligibility of the familiar voice. These results imply that the spatial pattern of activity in speech-sensitive regions reflects the intelligibility of a spoken sentence.