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U-Net has achieved a big success in various medical image segmentation applications. It requires to crop volumetric data into slices or patches for its training, resulting in loss of spatial and contextual information and challenges to segment target structures. This paper proposes an improved U-shape architecture called densely connected attention spatial-temporal U-Net. Specifically, such an architecture is created in accordance with several modules of dense connections, convolutional long short-term memory, and attention gates, fusing the advantages of these modules to precisely extract both spatialtemporal structural intra-slice and inter-slice contextual information. We applied our proposed method to segment the kidneys and main (external) renal arteries in 35 cases of patient kidney CT volumes, with the experimental results showing that our proposed method certainly outperforms current 2D and 3D fully convolutional networks. The average dice similarity coefficients of the kidneys and main renal arteries were improved from (95.48%, 81.11%) to (96.25%, 82.16%), respectively. Particularly, the amount of parameters were reduced from 34.88M to 13.49M.