Glioma refers to a highly prevalent type of brain tumor that is strongly associated with a high mortality rate. During the treatment process of the disease, it is particularly important to accurately perform segmentation of the glioma from Magnetic Resonance Imaging (MRI). However, existing methods used for glioma segmentation usually rely solely on either local or global features and perform poorly in terms of capturing and exploiting critical information from tumor volume features. Herein, we propose a local and global dual transformer with an attentional supervision U-shape network called DTASUnet, which is purposed for glioma segmentation. First, we built a pyramid hierarchical encoder based on 3D shift local and global transformers to effectively extract the features and relationships of different tumor regions. We also designed a 3D channel and spatial attention supervision module to guide the network, allowing it to capture key information in volumetric features more accurately during the training process. The experimental results show that DTASUnet exhibited superior or competitive performance compared to other state-of-the-art algorithms. In the BraTS 2018 validation set, the average Dice scores of DTASUnet for the tumor core (TC), whole tumor (WT), and enhancing tumor (ET) regions were 0.845, 0.905, and 0.808, respectively. For the BraTS 2020 validation set, the average Dice scores of TC, WT, and ET were 0.844, 0.906, and 0.790, respectively. These results demonstrate that DTASUnet has utility in assisting clinicians with determining the location of gliomas to facilitate more efficient and accurate brain surgery and diagnosis.