Although Graph Neural Networks (GNNs) have exhibited the powerful ability to gather graph-structured information from neighborhood nodes via various message-passing mechanisms, the performance of GNNs is limited by poor generalization and fragile robustness caused by noisy and redundant graph data. As a prominent solution, Graph Augmentation Learning (GAL) has recently received increasing attention. Among prior GAL approaches, edge-dropping methods that randomly remove edges from a graph during training are effective techniques to improve the robustness of GNNs. However, randomly dropping edges often results in bypassing critical edges, consequently weakening the effectiveness of message passing. In this paper, we propose a novel adversarial edge-dropping method (ADEdgeDrop) that leverages an adversarial edge predictor guiding the removal of edges, which can be flexibly incorporated into diverse GNN backbones. Employing an adversarial training framework, the edge predictor utilizes the line graph transformed from the original graph to estimate the edges to be dropped, which improves the interpretability of the edge-dropping method. The proposed ADEdgeDrop is optimized alternately by stochastic gradient descent and projected gradient descent. Comprehensive experiments on six graph benchmark datasets demonstrate that the proposed ADEdgeDrop outperforms state-of-the-art baselines across various GNN backbones, demonstrating improved generalization and robustness.