Objective. In recent years, methods based on U-shaped structure and skip connection have achieved remarkable results in many medical semantic segmentation tasks. However, the information integration capability of this structure is still limited due to the incompatibility of feature maps of encoding and decoding stages at corresponding levels and lack of extraction of valid information in the final stage of encoding. This structural defect is particularly obvious in segmentation tasks with non-obvious, small and blurred-edge targets. Our objective is to design a novel segmentation network to solve the above problems. Approach. The segmentation network named Global Context-Aware Network is mainly designed by inserting a Multi-feature Collaboration Adaptation (MCA) module, a Scale-Aware Mining (SAM) module and an Edge-enhanced Pixel Intensity Mapping (Edge-PIM) into the U-shaped structure. Firstly, the MCA module can integrate information from all encoding stages and then effectively acts on the decoding stages, solving the problem of information loss during downsampling and pooling. Secondly, the SAM module can further mine information from the encoded high-level features to enrich the information passed to the decoding stage. Thirdly, Edge-PIM can further refine the segmentation results by edge enhancement. Main results. We newly collect Magnetic Resonance Imaging of Colorectal Cancer Liver Metastases (MRI-CRLM) dataset in different imaging sequences with non-obvious, small and blurred-edge liver metastases. Our method performs well on the MRI-CRLM dataset and the publicly available ISIC-2018 dataset, outperforming state-of-the-art methods such as CPFNet on multiple metrics after boxplot analysis, indicating that it can perform well on a wide range of medical image segmentation tasks. Significance. The proposed method solves the problem mentioned above and improved segmentation accuracy for non-obvious, small and blurred-edge targets. Meanwhile, the proposed visualization method Edge-PIM can make the edge more prominent, which can assist medical radiologists in their research work well.