The left superior temporal cortex shows greater responsiveness to speech than to non-speech sounds according to previous neuroimaging studies, suggesting that this brain region has a special role in speech processing. However, since speech sounds differ acoustically from the non-speech sounds, it is possible that this region is not involved in speech perception per se, but rather in processing of some complex acoustic features. "Sine wave speech" (SWS) provides a tool to study neural speech specificity using identical acoustic stimuli, which can be perceived either as speech or non-speech, depending on previous experience of the stimuli. We scanned 21 subjects using 3T functional MRI in two sessions, both including SWS and control stimuli. In the pre-training session, all subjects perceived the SWS stimuli as non-speech. In the post-training session, the identical stimuli were perceived as speech by 16 subjects. In these subjects, SWS stimuli elicited significantly stronger activity within the left posterior superior temporal sulcus (STSp) in the post- vs. pre-training session. In contrast, activity in this region was not enhanced after training in 5 subjects who did not perceive SWS stimuli as speech. Moreover, the control stimuli, which were always perceived as non-speech, elicited similar activity in this region in both sessions. Altogether, the present findings suggest that activation of the neural speech representations in the left STSp might be a pre-requisite for hearing sounds as speech.