Language acquisition in the first year of life plays an important role in human development. Although recent research has increased our knowledge of early language development, the origins and developmental trajectories of language processing during infancy are still being debated. One important issue is whether the infant brain has already developed adult-like functional cortical specialization and lateralization for speech and language processing. Although a relatively large number of previous studies have investigated the cortical specialization for speech processing in newborns by comparing responses to normal speech with responses to time-reversed speech as a control, the subsequent development of this differential response is less well understood. In the current study, our primary goal was, therefore, to expand our knowledge of functional specialization for speech during the first year of life. By using functional near-infrared spectroscopy (fNIRS), we examined the hemodynamic responses in the temporal cortex to forward-going speech in the native language, Dutch, and backward Dutch in seventy-eight infants aged 5 and 10 months. We observed that five-month-old infants show bilateral activation to both forward and backward speech without obvious hemispheric lateralization for language, while ten-month-old infants show greater leftlateralized inverted responses (e.g., reduction in oxyhaemoglobin and increase in deoxyhaemoglobin) to forward speech than to backward speech. Overall, our findings indicate that the neural correlates of language processing undergo developmental changes in the first year of life.