Brain networks characterize complex connectivities among brain regions as graph structures, which provide a powerful means to study brain diseases. In recent years, graph neural networks have emerged as a prevalent paradigm of learning with structured data. However, most brain network datasets are limited in sample sizes due to the relatively high cost of data collection, which hinders the deep learning models from sufficient training. Inspired by meta-learning that learns new concepts fast with limited training examples, this paper studies data efficient training strategies for analyzing brain networks in a cross-dataset setting. Specifically, we propose to meta-train the model on datasets of large sample sizes and transfer the knowledge to small datasets. In addition, we also explore brain-network-oriented design considerations, including atlas mapping and adaptive task reweighing. Compared to other pre-training strategies, our meta-learning-based approach achieves higher and stabler performance, which demonstrates the effectiveness of our proposed solutions. The framework is also able to derive new insights regarding the similarities among datasets and diseases in a data-driven fashion.