This study assessed cortical tracking of temporal information in incoming natural speech in seven-month-old infants. Cortical tracking refers to the process by which neural activity follows the dynamic patterns of the speech input. In adults, it has been shown to involve attentional mechanisms and to facilitate effective speech encoding. However, in infants, cortical tracking or its effects on speech processing have not been investigated. This study measured cortical tracking of speech in infants and, given the involvement of attentional mechanisms in this process, cortical tracking of both infant-directed speech (IDS), which is highly attractive to infants, and the less captivating adult-directed speech (ADS), were compared. IDS is the speech register parents use when addressing young infants. In comparison to ADS, it is characterised by several acoustic qualities that capture infants' attention to linguistic input and assist language learning. Seven-month-old infants' cortical responses were recorded via electroencephalography as they listened to IDS or ADS recordings. Results showed stronger low-frequency cortical tracking of the speech envelope in IDS than in ADS. This suggests that IDS has a privileged status in facilitating successful cortical tracking of incoming speech which may, in turn, augment infants' early speech processing and even later language development.