Children with Down's syndrome (DS) might exhibit disrupted brain functional connectivity in the motor and prefrontal cortex. To inspect the alterations in brain activation and functional connectivity for children with DS, the functional near-infrared spectroscopy (fNIRS) method was applied to examine the brain activation difference in the motor and prefrontal cortex between the DS and typically developing (TD) groups during a fine motor task. In addition, small-world analysis based on graph theory was also carried out to characterize the topological organization of functional brain networks. Interestingly, behavior data demonstrated that the DS group showed significantly long reaction time and low accuracy as compared to the TD group (p < 0.05). More importantly, significantly reduced brain activations in the frontopolar area, the pre-motor, and the supplementary motor cortex (p < 0.05) were identified in the DS group compared with the TD group. Meanwhile, significantly high global efficiency (E) and short average path length (L) were also detected for the DS group. This pilot study illustrated that the disrupted connectivity of frontopolar area, pre-motor, and supplementary motor cortex might be one of the core mechanisms associated with motor and cognitive impairments for children with DS. Therefore, the combination of the fNIRS technique with functional network analysis may pave a new avenue for improving our understanding of the neural mechanisms of DS.