Human infants rapidly develop their auditory perceptual abilities and acquire culture-specific knowledge in speech and music in the second 6 months of life. In the adult brain, neural rhythm around 10 Hz in the temporal lobes is thought to reflect sound analysis and subsequent cognitive processes such as memory and attention. To study when and how such rhythm emerges in infancy, we examined electroencephaolgram (EEG) recordings in infants 4 and 12 months of age during sound stimulation and silence. In the 4-month-olds, the amplitudes of narrowly tuned 4-Hz brain rhythm, recorded from bilateral temporal electrodes, were modulated by sound stimuli. In the 12-month-olds, the sound-induced modulation occurred at faster 6-Hz rhythm at temporofrontal locations. The brain rhythms in the older infants consisted of more complex components, as even evident in individual data. These findings suggest that auditory-specific rhythmic neural activity, which is already established before 6 months of age, involves more speed-efficient long-range neural networks by the age of 12 months when long-term memory for native phoneme representation and for musical rhythmic features is formed. We suggest that maturation of distinct rhythmic components occurs in parallel, and that sensory-specific functions bound to particular thalamo-cortical networks are transferred to newly developed higher-order networks step by step until adult hierarchical neural oscillatory mechanisms are achieved across the whole brain.