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Kidney structures segmentation is a crucial yet challenging task in the computer-aided diagnosis of surgery-based renal cancer. Although numerous deep learning models have achieved remarkable success in many medical image segmentation tasks, accurate segmentation of kidney structures on computed tomography angiography (CTA) images remains challenging, due to the variable sizes of kidney tumors and the ambiguous boundaries between kidney structures and their surroundings. In this paper, we propose a boundary-aware network (BA-Net) to segment kidneys, kidney tumors, arteries, and veins on CTA scans. This model contains a shared encoder, a boundary decoder, and a segmentation decoder. The multi-scale deep supervision strategy is adopted on both decoders, which can alleviate the issues caused by variable tumor sizes. The boundary probability maps produced by the boundary decoder at each scale are used as attention to enhance the segmentation feature maps. We evaluated the BA-Net on the Kidney PArsing (KiPA) Challenge dataset and achieved an average Dice score of 89.65$\%$ for kidney structure segmentation on CTA scans using 4-fold cross-validation. The results demonstrate the effectiveness of the BA-Net.