Vessel segmentation is critical for disease diagnosis and surgical planning. Recently, the vessel segmentation method based on deep learning has achieved outstanding performance. However, vessel segmentation remains challenging due to thin vessels with low contrast that easily lose spatial information in the traditional U-shaped segmentation network. To alleviate this problem, we propose a novel and straightforward full-resolution network (FR-UNet) that expands horizontally and vertically through a multiresolution convolution interactive mechanism while retaining full image resolution. In FR-UNet, the feature aggregation module integrates multiscale feature maps from adjacent stages to supplement high-level contextual information. The modified residual blocks continuously learn multiresolution representations to obtain a pixel-level accuracy prediction map. Moreover, we propose the dual-threshold iterative algorithm (DTI) to extract weak vessel pixels for improving vessel connectivity. The proposed method was evaluated on retinal vessel datasets (DRIVE, CHASE_DB1, and STARE) and coronary angiography datasets (DCA1 and CHUAC). The results demonstrate that FR-UNet outperforms state-of-the-art methods by achieving the highest Sen, AUC, F1, and IOU on most of the above-mentioned datasets with fewer parameters, and that DTI enhances vessel connectivity while greatly improving sensitivity. The code is available at: https://github.com/lseventeen/FR-UNet.