This paper introduces EU-Net, an efficient and enhanced U-Net-like architecture designed for medical image segmentation. It comprises a lightweight encoder and decoder connected through dense skip-connections. To further improve the robustness of the EU-Net, chain EU-Net is proposed. Chain EU-Net is based on a streamlined architecture that uses multiple EU-Net to build light weight deep neural networks by dense skip-connection. Compared to traditional segmentation algorithms such as U-Net and its variants, our neural network structure possesses both lightweight and stability simultaneously. EU-Net and chain EU-Net are evaluated on three typical medical image segmentation tasks: GLAS (Gland segmentation) dataset, RITE (Retinal Images Vessel Tree Extraction) dataset and LiTS (Liver Tumor Segmentation Challenge) dataset. In addition, we used PUFH (Peking University First Hospital) dataset. Experimental results show that the proposed methods achieve state-of-the-art performance with very few parameters.