Brain functional connectivity (BFC) built from resting-state functional magnetic resonance imaging (rs-fMRI) has shown promising results in revealing the pathological basis of neurological disorders. However, a major problem is that existing approaches tend to limit analysis to a single scale, which unmatches the truth that modern neuroscience highlights BFC as a multi-scale topological architecture. Such a narrow view does lose representation of the inherent BFC topology and would weaken its performance. To solve this issue, we propose a novel triple-pooling graph neural network (TPGNN) to learn different scales of BFC topological knowledge in a task-adaptive way. Specifically, a pooling architecture with triple branches is designed to automate BFC analysis on the global scale, community scale, and region of interest (ROI) scale, respectively. We validate the diagnostic performance of TPGNN on an open autism spectrum disorder (ASD) dataset. Experimental results demonstrate that TPGNN outperforms the alternative state-of-the-art BFC analysis methods and provides potential biomarkers of different scales to benefit neuroscience.