Fundus vessel segmentation is vital for diagnosing ophthalmic diseases like central serous chorioretinopathy (CSC), diabetic retinopathy, and glaucoma. Accurate segmentation provides crucial vessel morphology details, aiding the early detection and intervention of ophthalmic diseases. However, current algorithms struggle with fine vessel segmentation and maintaining sensitivity in complex regions. Challenges also stem from imaging variability and poor generalization across multimodal datasets, highlighting the need for more advanced algorithms in clinical practice. This paper aims to explore a new vessel segmentation method to alleviate the above problems. We propose a fundus vessel segmentation model based on a combination of double skip connections, deep supervision, and TransUNet, namely DS2TUNet. Initially, the original fundus images are improved through grayscale conversion, normalization, histogram equalization, gamma correction, and other preprocessing techniques. Subsequently, by utilizing the U-Net architecture, the preprocessed fundus images are segmented to obtain the final vessel information. Specifically, the encoder firstly incorporates the ResNetV1 downsampling, dilated convolution downsampling, and Transformer to capture both local and global features, which upgrades its vessel feature extraction ability. Then, the decoder introduces the double skip connections to facilitate upsampling and refine segmentation outcomes. Finally, the deep supervision module introduces multiple upsampling vessel features from the decoder into the loss function, so that the model can learn vessel feature representations more effectively and alleviate gradient vanishing during the training phase. Extensive experiments on publicly available multimodal fundus datasets such as DRIVE, CHASE_DB1, and ROSE-1 demonstrate that the DS2TUNet model attains F1-scores of 0.8195, 0.8362, and 0.8425, with Accuracy of 0.9664, 0.9741, and 0.9557, Sensitivity of 0.8071, 0.8101, and 0.8586, and Specificity of 0.9823, 0.9869, and 0.9713, respectively. Additionally, the model also exhibits excellent test performance on the clinical fundus dataset CSC, with F1-score of 0.7757, Accuracy of 0.9688, Sensitivity of 0.8141, and Specificity of 0.9801 based on the weight trained on the CHASE_DB1 dataset. These results comprehensively validate that the proposed method obtains good performance in fundus vessel segmentation, thereby aiding clinicians in the further diagnosis and treatment of fundus diseases in terms of effectiveness and feasibility.