Medical image segmentation is a critical task used to accurately extract regions of interest and pathological areas from medical images. In recent years, significant progress has been made in the field of medical image segmentation using deep learning and neural networks. However, existing methods still have limitations in terms of fusing local features and global contextual information due to the complex variations and irregular shapes of medical images. To address this issue, this paper proposes a medical image segmentation architecture called LGI Net, which improves the internal computation to achieve sufficient interaction between local perceptual capabilities and global contextual information within the network. Furthermore, the network incorporates an ECA module to effectively capture the interplay between channels and improve inter-layer information exchange capabilities. We conducted extensive experiments on three public medical image datasets: Kvasir, ISIC, and X-ray to validate the effectiveness of the proposed method. Ablation studies demonstrated the effectiveness of our LGAF, and comparative experiments confirmed the superiority of our proposed LGI Net in terms of accuracy and parameter efficiency. This study provides an innovative approach in the field of medical image segmentation, offering valuable insights for further improvements in accuracy and performance. The code and models will be available at https://github.com/LiuLinjie0310/LGI-Net.