Background: Vessel segmentation is a fundamental, yet not well-solved problem in medical image analysis, due to complicated geometrical and topological structures of human vessels. Unlike existing rule- and conventional learning-based techniques, which hardly capture the location of tiny vessel structures and perceive their global spatial structures, Methods: we propose Simultaneous Self- and Channel-attention Neural Network (termed SSCA-Net) to solve the multi-scale structure-preserving vessel segmentation (MSVS) problem. SSCA-Net differs from the conventional neural networks in modeling image global contexts, showing more power to understand the global semantic information by both self- and channel-attention (SCA) mechanism, and offering high performance on segmenting vessels with multi-scale structures. Specifically, the SCA module is designed and embedded in the feature decoding stage to learn SCA features at different layers, which the self-attention is used to obtain the position information of the feature itself, and the channel attention is designed to guide the shallow features to obtain global feature information. Results: Three blood vessel data sets are train and validate the models. our SSCA-Net achieves 96.21% in Dic and 92.70% in Mean IoU on the intracranial vessel dataset and achieved 98.20 %, 83.52% and 96.14% in AUC, Sen and Acc respectively on retinal vessel dataset. The obtain model can segment the leg arteries and Dic score is 97.21% and the Mean IoU score is 94.42%. Conclusions: The results demonstrated that the proposed SSCA-Net clear improvements of our method over the state-of-the-arts in terms of preserving vessel details and global spatial structures.