The sliding-window-based dynamic functional connectivity network (D-FCN) has been becoming an increasingly useful tool for understanding the changes of brain connectivity patterns and the association of neurological diseases with these dynamic variations. However, conventional D-FCN is essentially low-order network, which only reflects the pairwise interaction pattern between brain regions and thus overlooking the high-order interactions among multiple brain regions. In addition, D-FCN is innate with temporal sensitivity issue, i.e., D-FCN is sensitive to the chronological order of its subnetworks. To deal with the above issues, we propose a novel high-order functional connectivity network framework based on the central moment feature of D-FCN. Specifically, we firstly adopt a central moment approach to extract multiple central moment feature matrices from D-FCN. Furthermore, we regard the matrices as the profiles to build multiple high-order functional connectivity networks which further capture the higher level and more complex interaction relationships among multiple brain regions. Finally, we use the voting strategy to combine the high-order networks with D-FCN for autism spectrum disorder diagnosis. Experimental results show that the combination of multiple functional connectivity networks achieves accuracy of 88.06%, and the best single network achieves accuracy of 79.5%.