Brain functional connectivity (FC) derived from resting-state functional MRI (rs-fMRI) data has become a powerful approach to measure and map brain activity. Using fMRI data, graph convolutional network (GCN) has recently shown its superiority in learning discriminative representations of brain FC networks. However, existing studies typically utilize one specific template to partition the brain into multiple regions-of-interest (ROIs) for constructing FCs, which may limit the analysis to a single spatial scale (i.e., a fixed graph) determined by the template. Also, previous methods usually ignore the underlying high-order (e.g., triplet) association among subjects. To this end, we propose a multi-scale triplet graph convolutional network (MTGCN) for brain functional connectivity analysis with rs-fMRI data. Specifically, we first employ multi-scale templates for coarse-to-fine ROI parcellation to construct multi-scale FCs for each subject. We then develop a triplet GCN (TGCN) model to learn multi-scale graph representations of brain FC networks, followed by a weighted fusion scheme for classification. Experimental results on 1,218 subjects suggest the efficacy or our method.