The cingulo-opercular (CO) and frontoparietal (FP) networks are part of the cognitive-control system of the brain. Evidence suggests that over the course of development, brain regions supporting cognitive-control functions become more integrated within their networks (i.e., have increased within-network connectivity), more separated from other networks, and, due to increased maturation along development, are more functionally connected between the networks. The focus of this study was to characterize the developmental trajectory of the CO and FP networks from early infancy (17 months) to 9 years of age in typically developing children while listening to stories, using functional connectivity analyses. Seventy-four children underwent a functional magnetic resonance imaging session while listening to stories inside the scanner. Within-and between-network functional connectivity and graph theory measures were compared during development. Developmental increase in functional connectivity within the CO network and between the CO and FP networks, as well as global efficiency of the CO network from 17 months to 9 years of age, was observed. These findings highlight the involvement of the CO and FP networks in story listening from early infancy, which increases along development. Future studies examining failures in language acquisition to further explore the role of these networks in story listening are warranted.