Functional neuroimaging has been used to show that the developing auditory cortex of very young human infants responds, in some way, to sound. However, impoverished stimuli and uncontrolled designs have made it difficult to attribute brain responses to specific auditory features, and thus made it difficult to assess the maturity of feature tuning in auditory cortex. To address this, we used functional magnetic resonance imaging (fMRI) to measure the brain activity evoked by naturalistic sounds (a series of sung lullabies) in two groups of infants (3 and 9 months) and adults. We developed a novel analysis method – inter-subject regression (ISR) – to quantify the similarity of cortical responses between infants and adults, and to decompose components of the response due to different auditory features. We found that the temporal pattern of activity in infant auditory cortex shared similarity with adults. Some of this shared response could be attributed to simple acoustic features, such as frequency, pitch, envelope, but other parts were not, suggesting that even more complex adult-like features are represented in auditory cortex in early infancy.