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Retinal artery/vein (A/V) classification lays the foundation for the quantitative analysis of retinal vessels, which is associated with potential risks of various cardiovascular and cerebral diseases. The topological connection relationship, which has been proved effective in improving the A/V classification performance for the conventional graph based method, has not been exploited by the deep learning based method. In this paper, we propose a Topology Ranking Generative Adversarial Network (TR-GAN) to improve the topology connectivity of the segmented arteries and veins, and further to boost the A/V classification performance. A topology ranking discriminator based on ordinal regression is proposed to rank the topological connectivity level of the ground-truth, the generated A/V mask and the intentionally shuffled mask. The ranking loss is further back-propagated to the generator to generate better connected A/V masks. In addition, a topology preserving module with triplet loss is also proposed to extract the high-level topological features and further to narrow the feature distance between the predicted A/V mask and the ground-truth. The proposed framework effectively increases the topological connectivity of the predicted A/V masks and achieves state-of-the-art A/V classification performance on the publicly available AV-DRIVE dataset.