With the increasing popularity of graph-based learning, graph neural networks (GNNs) emerge as the essential tool for gaining insights from graphs. However, unlike the conventional CNNs that have been extensively explored and exhaustively tested, people are still worrying about the GNNs' robustness under the critical settings, such as financial services. The main reason is that existing GNNs usually serve as a black-box in predicting and do not provide the uncertainty on the predictions. On the other side, the recent advancement of Bayesian deep learning on CNNs has demonstrated its success of quantifying and explaining such uncertainties to fortify CNN models. Motivated by these observations, we propose UAG, the first systematic solution to defend adversarial attacks on GNNs through identifying and exploiting hierarchical uncertainties in GNNs. UAG develops a Bayesian uncertainty technique to explicitly capture uncertainties in GNNs and further employs an uncertainty-aware attention technique to defend adversarial attacks on GNNs. Intensive experiments show that our proposed defense approach outperforms the state-of-the-art solutions by a significant margin.