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As one of the popular deep learning methods, deep convolutional neural networks (DCNNs) have been widely adopted in segmentation tasks and have received positive feedback. However, in segmentation tasks, DCNN-based frameworks are known for their incompetence in dealing with global relations within imaging features. Although several techniques have been proposed to enhance the global reasoning of DCNN, these models are either not able to gain satisfying performances compared with traditional fully-convolutional structures or not capable of utilizing the basic advantages of CNN-based networks (namely the ability of local reasoning). In this study, compared with current attempts to combine FCNs and global reasoning methods, we fully extracted the ability of self-attention by designing a novel attention mechanism for 3D computation and proposed a new segmentation framework (named 3DTU) for three-dimensional medical image segmentation tasks. This new framework processes images in an end-to-end manner and executes 3D computation on both the encoder side (which contains a 3D transformer) and the decoder side (which is based on a 3D DCNN). We tested our framework on two independent datasets that consist of 3D MRI and CT images. Experimental results clearly demonstrate that our method outperforms several state-of-the-art segmentation methods in various metrics.