Brain networks/graphs derived from resting-state functional MRI (fMRI) help study underlying pathophysiology of neurocognitive disorders by measuring neuronal activities in the brain. Some studies utilize learning-based methods for brain network analysis, but typically suffer from low model generalizability caused by scarce labeled fMRI data. As a notable self-supervised strategy, graph contrastive learning helps leverage auxiliary unlabeled data. But existing methods generally arbitrarily perturb graph nodes/edges to generate augmented graphs, without considering essential topology information of brain networks. To this end, we propose a topology-aware graph augmentation (TGA) framework, comprising a pretext model to train a generalizable encoder on large-scale unlabeled fMRI cohorts and a task-specific model to perform downstream tasks on a small target dataset. In the pretext model, we design two novel topology-aware graph augmentation strategies: (1) hub-preserving node dropping that prioritizes preserving brain hub regions according to node importance, and (2) weight-dependent edge removing that focuses on keeping important functional connectivities based on edge weights. Experiments on 1, 688 fMRI scans suggest that TGA outperforms several state-of-the-art methods.