From diagnosing cardiovascular diseases to analyzing the progression of diabetic retinopathy, accurate retinal artery/vein (A/V) classification is critical. Promising approaches for A/V classification, ranging from conventional graph based methods to recent convolutional neural network (CNN) based models, have been known. However, the inability of traditional graph based methods to utilize deep hierarchical features extracted by CNNs and the limitations of current CNN based methods to incorporate vessel topology information hinder their effectiveness. In this paper, we propose a new CNN based framework, VTG-Net (vessel topology graph network), for retinal A/V classification by incorporating vessel topology information. VTG-Net exploits retinal vessel topology along with CNN features to improve A/V classification accuracy. Specifically, we transform vessel features extracted by CNN in the image domain into a graph representation preserving the vessel topology. Then by exploiting a graph convolutional network (GCN), we enable our model to learn both CNN features and vessel topological features simultaneously. The final predication is attained by fusing the CNN and GCN outputs. Using a publicly available AV-DRIVE dataset and an in-house dataset, we verify the high performance of our VTG-Net for retinal A/V classification over state-of-the-art methods (with ~2% improvement in accuracy on the AV-DRIVE dataset).