Functional magnetic resonance imaging (fMRI) permits detailed study of human brain function. Understanding the age-specific development of neural circuits in the typically developing brain may help us generate new hypotheses for developmental psychopathologies. Functional connectivity (FC), defined as the statistical associations between two brain regions, has been widely used in estimating functional networks from fMRI data. Previous research has shown that the evolution of FC does not follow a linear trend, particularly from childhood to young adulthood. Thus, this work aims to detect the nuanced FC changes with age from the non-linear curves and identify age-period-specific FC development patterns. We proposed a sliding-window based clustering approach to identify refined age interval of FC development. We used resting-state fMRI (rs-fMRI) data from the human connectome project-development (HCP-D), which recruited children, adolescents, and young adults aged from 5 to 21 years. Our analyses revealed different developmental patterns of resting-state FC by sex. In general, females matured earlier than males, but males had a faster development rate during age 100-120 months. We identified four developmental phases: network construction in late childhood, segregation and integration construction in adolescence, network pruning in young adulthood, and a unique phase in males -- U-shape development. In addition, we investigated the sex effect on the slopes of FC-age correlation. Males had higher slopes during late childhood and young adulthood. These results inform trajectories of normal FC development, information that can in the future be used to pinpoint when development might go awry in neurodevelopmental disorders.