The accurate gland segmentation from digitized H&E (hematoxylin and eosin) histology images with a wide range of histologic grades of cancer is quite challenging. In recent years, several fully convolutional network methods have been proposed, with UNet being the most classic. The UNet model, with its symmetric structure, has shown excellent performance in gland segmentation tasks. However, the locality of convolution operations in UNet also limits its ability to capture global dependencies. To address this limitation, this paper proposes a novel deep glandular tissue image segmentation network based on Swin UNet, termed EMA-Swin UNet. This network replaces CNN modules with Swin Transformer modules to capture both local and global representations. Additionally, the EMA-Swin UNet incorporates an Efficient Multi-scale Attention (EMA) module to enhance multi-scale feature extraction for glandular tissues of various sizes by capturing global dynamic features and long-range smooth features from the encoder outputs. By integrating edge-detection pooling, we enhanced the refinement of prediction maps produced by the EMA-Swin UNet. Moreover, we standardized the staining across both the ClaS dataset and the six-grade tumor differentiation dataset from EBHI-Seg using Reinhard normalization. The final segmentation results are compared with those of classical gland segmentation algorithms on the ClaS and EBHI-Seg datasets, demonstrating the effectiveness of our proposed method. Particularly, on the GlaS dataset, the mDice reached 0.894.