Segmentation is a fundamental task in medical image analysis. However, most existing methods focus on primary region extraction and ignore edge information, which is useful for obtaining accurate segmentation. In this paper, we propose a generic medical segmentation method, called Edge-aTtention guidance Network (ET-Net), which embeds edge-attention representations to guide the segmentation network. Specifically, an edge guidance module is utilized to learn the edge-attention representations in the early encoding layers, which are then transferred to the multi-scale decoding layers, fused using a weighted aggregation module. The experimental results on four segmentation tasks (i.e., optic disc/cup and vessel segmentation in retinal images, and lung segmentation in chest X-Ray and CT images) demonstrate that preserving edge-attention representations contributes to the final segmentation accuracy, and our proposed method outperforms current state-of-the-art segmentation methods. The source code of our method is available at https://github.com/ZzzJzzZ/ETNet.