During childhood, the brain is gradually converging to the efficient functional architecture observed in adults. How the brain's functional architecture evolves with age, particularly in young children, is however, not well understood. We examined the functional connectivity of the core language regions, in association with cortical growth and language abilities, in 175 young children in the age range of 4 to 9 years. We analyzed the brain's developmental changes using resting-state functional and T1-weighted structural magnetic resonance imaging data. The results showed increased functional connectivity strength with age between the pars triangularis of the left inferior frontal gyrus and left temporoparietal regions (cohen's d = 0.54, CI: 0.24 - 0.84), associated with children's language abilities. Stronger functional connectivity between bilateral prefrontal and temporoparietal regions was associated with better language abilities regardless of age. In addition, the stronger functional connectivity between the left inferior frontal and temporoparietal regions was associated with larger surface area and thinner cortical thickness in these regions, which in turn was associated with superior language abilities. Thus, using functional and structural brain indices, coupled with behavioral measures, we elucidate the association of functional language network development, language ability, and cortical growth, thereby adding to our understanding of the neural basis of language acquisition in young children.