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In contrast to the fully supervised methods using pixel-wise mask labels, box-supervised instance segmentation takes advantage of the simple box annotations, which has recently attracted a lot of research attentions. In this paper, we propose a novel single-shot box-supervised instance segmentation approach, which integrates the classical level set model with deep neural network delicately. Specifically, our proposed method iteratively learns a series of level sets through a continuous Chan-Vese energy-based function in an end-to-end fashion. A simple mask supervised SOLOv2 model is adapted to predict the instance-aware mask map as the level set for each instance. Both the input image and its deep features are employed as the input data to evolve the level set curves, where a box projection function is employed to obtain the initial boundary. By minimizing the fully differentiable energy function, the level set for each instance is iteratively optimized within its corresponding bounding box annotation. The experimental results on four challenging benchmarks demonstrate the leading performance of our proposed approach to robust instance segmentation in various scenarios. The code is available at: https://github.com/LiWentomng/boxlevelset.