Most analyses on functional brain connectivity across a group of brains are under the assumption that the positions of the voxels are aligned into a common space. However, the alignment errors are inevitable. To address such issue, a distributional representation for resting-state functional brain connectivity is proposed here. Unlike other relevant connectivity analyses that only consider connections with higher correlation values between voxels, the distributional approach takes the whole picture. The spatial structure of connectivity is captured by the distance between voxels so that the relative position information is preserved. The distributional representation can be visualized to find outliers in a large dataset. The centroid of a group of brains is discovered. The experimental results show that resting-state brains are distributed on the ‘orbit’ around their categorical centroid. In contrast to the main-stream representation such as selected network properties for disease classification, the proposed representation is task-free, which provides a promising foundation for further analysis on functional brain connectivity in various ends.