Skilled reading requires the convergent brain network between spoken language and reading. Here, we examined the developmental changes in this convergent network between beginning and skilled readers. We used fMRI data from 41 adults (aged from 20 to 21 years) and 21 children (aged from 9 to 12 years) who performed a Chinese word sound matching task in speech and print. Three complementary analytic approaches, including print-speech conjunction analysis, brain-behavioral analysis, and functional connectivity analysis were performed to reveal the link between print and speech neural systems as well as the developmental changes in this link. We found that (1) adults showed broader convergence than children; (2) coactivation in anterior dorsal regions (i.e., inferior frontal gyrus and insula) predominated in children, while coactivation in the ventral posterior region (i.e., middle temporal gyrus) predominated in adults, which aligns with the dual-stream model of reading; and (3) print-speech convergence regions showed task-specific functional connectivity patterns and there was an increased visual-modal specialization in the functional connectivity patterns with reading development. Our study provides important evidence for developmentally increased coactivation in ventral posterior regions and increased task specialization in print-speech convergence regions, which is crucial for successful reading.