One of the interesting issues in drug-target interaction studies is the activity cliff (AC), which is usually defined as structurally similar compounds with large differences in activity toward a common target. The AC is of great interest in medicinal chemistry as it may provide clues to understanding the complex properties of the target proteins, paving the way for practical applications aimed at the discovery of more potent drugs. In this paper, we propose graph convolutional networks for the prediction of AC and designate the proposed models as Activity Cliff prediction using Graph Convolutional Networks (ACGCNs). The results show that ACGCNs outperform several off-the-shelf methods when predicting ACs of three popular target data sets for thrombin, Mu opioid receptor, and melanocortin receptor. Finally, we utilize gradient-weighted class activation mapping to visualize activation weights at nodes in the molecular graphs, demonstrating its potential to contribute to the ability to identify important substructures for molecular docking.