The human cerebral cortex exhibits intricate interareal functional synchronization at the macroscale, with substantial individual variability in these functional connections. However, the spatial organization of functional connectivity (FC) variability across the human connectome edges and its significance in cognitive development remain unclear. Here, we identified a connectional axis in the edge-level FC variability. The variability declined continuously along this axis from within-network to between-network connections and from the edges linking association networks to those linking the sensorimotor and association networks. This connectional axis of functional variability is associated with spatial pattern of structural connectivity variability. Moreover, the connectional variability axis evolves in youth with an flatter axis slope. We also observed that the slope of the connectional variability axis was positively related to the performance in the higher-order cognition. Together, our results reveal a connectional axis in functional variability that is linked with structural connectome variability, refines during development, and is relevant to cognition.