The acoustic dimensions that distinguish speech sounds (like the vowel differences in “boot” and “boat”) also differentiate speakers’ voices. Therefore, listeners must normalize across speakers without losing linguistic information. Past behavioral work suggests an important role for auditory contrast enhancement in normalization: preceding context affects listeners’ perception of subsequent speech sounds. Here, using intracranial electrocorticography in humans, we investigate whether and how such context effects arise in auditory cortex. Participants identified speech sounds that were preceded by phrases from two different speakers whose voices differed along the same acoustic dimension as target words (the lowest resonance of the vocal tract). In every participant, target vowels evoke a speaker-dependent neural response that is consistent with the listener’s perception, and which follows from a contrast enhancement model. Auditory cortex processing thus displays a critical feature of normalization, allowing listeners to extract meaningful content from the voices of diverse speakers.