The cortical network for language processing consists of the frontal, temporal, and parietal regions of the brain. While it is probable that an early precursor of this network is responsible for language acquisition, the characteristics of the network during development have not been fully investigated. In the present study, the organization of this functional network was examined in infant brains. Twenty full-term healthy infants (104–123 days old) participated in this study. All infants were asleep during testing. Cortical activation was measured using 94-channel near-infrared spectroscopy (NIRS). Japanese speech sounds (duration: ~4 s) were presented to the infants every 10 or 20 s (63 sentences over 920 s). We calculated the correlation coefficients between a continuous time course of oxygenated hemoglobin (oxy-Hb) signals, obtained from a single channel, and that of all other channels. Continuous data were filtered using multiple band-pass filters (0.009–0.2, 0.009–0.04, or 0.04–0.2 Hz) prior to analysis. We also applied sliding time-window analyses (3-min window with 2-min overlap), in which we calculated correlations within each of the thirteen 3-min time bins. Based on these correlation coefficients, we calculated eigenvector centrality values. These analyses revealed that the left frontal and temporoparietal regions had high eigenvector centrality values. While a ventral portion of the inferior frontal region consistently showed high centrality in all frequency bands, the dorsal inferior frontal region showed high values in the highest frequency band, which may correspond to frequencies related to hemodynamic responses to speech. The values in the temporoparietal hubs observed in the highest band were dependent on the timing of recording (i.e., time window). Our findings suggest that the left frontal and temporoparietal regions are cortical hubs of the language network even in the developing brain. These hubs play distinct roles during speech processing; the ventral frontal hub acts as a base, regardless of external stimuli, and the activity of the dorsal frontal and temporoparietal hubs is modulated by language information.