Retinal vessel segmentation plays a key role in computer-aided screening, diagnosis, and treatment of various cardiovascular and ophthalmic diseases. Recently, deep learning-based retinal vessel segmentation algorithms have achieved remarkable performance. However, due to the domain shift problem, the performance of these algorithms often degrades when they are applied to new data that is different from the training data. Manually labeling new data for each test domain is often a time-consuming and laborious task. In this work, we explore unsupervised domain adaptation in retinal vessel segmentation by using entropy-based adversarial learning and transfer normalization layer to train a segmentation network, which generalizes well across domains and requires no annotation of the target domain. Specifically, first, an entropy-based adversarial learning strategy is developed to reduce the distribution discrepancy between the source and target domains while also achieving the objective of entropy minimization on the target domain. In addition, a new transfer normalization layer is proposed to further boost the transferability of the deep network. It normalizes the features of each domain separately to compensate for the domain distribution gap. Besides, it also adaptively selects those feature channels that are more transferable between domains, thus further enhancing the generalization performance of the network. We conducted extensive experiments on three regular fundus image datasets and an ultra-widefield fundus image dataset, and the results show that our approach yields significant performance gains compared to other state-of-the-art methods.