Accurate segmentation of retinal blood vessels from retinal images is crucial to aid in the detection and diagnosis of many eye diseases. In this paper, a fusion network based on the dual attention mechanism and atrous spatial pyramid pooling (DAANet) is proposed for vessel segmentation. First, we propose a dual attention module consisting of a position attention module and a channel attention module, which aims to adaptively recalibrate features to extract effective features. And full-scale skip connections are used in the encoder to provide multi-scale feature maps for the dual attention modules. Then, atrous spatial pyramid pooling (ASPP) allows the network to capture features at multiple scales and combine high-level semantic information with low-level features through the encoder-decoder architecture. We qualitatively evaluate the model using five metrics: sensitivity, specificity, accuracy, AUC, and F1 score on DRIVE, CHASED_B1, and STARE datasets. The DAANet outperforms the work of 10 state-of-the-art predecessors in these three datasets. Furthermore, we apply the trained model to clinical retinal images. The model obtains gratifying accurate and detailed segmentation results, which demonstrates a promising application prospect in medical practices.