During the first 6-7 years of life children undergo a period of major neurocognitive development. Higher-order cognitive functions such as executive control of attention, encoding and retrieving of stored information and goal-directed behavior are present but less developed compared to older individuals. There is only very limited information from functional magnetic resonance imaging (fMRI) studies about the level of organization of functional networks in children in the early school period. In this study we perform continuous resting-state functional connectivity MRI in 5- to 8-year-old children in an awake state to identify and characterize resting-state networks (RSNs). Temporal concatenation independent component analysis (ICA) approach was applied to analyze the data. We identified 14 components consisting of regions known to be involved in visual and auditory processing, motor function, attention control, memory, and the default mode network (DMN). Most networks, in particular those supporting basic motor function and sensory related processing, had a robust functional organization similar to mature adult patterns. In contrast, the DMN and other RSNs involved in higher-order cognitive functions had immature characteristics, revealing incomplete and fragmented patterns indicating less developed functional connectivity. We therefore conclude that the DMN and other RSNs involved in higher order cognitive functioning are detectable, yet in an immature state, at an age when these cognitive abilities are mastered.