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The shape and location of the orbital tumor are very valuable for tumor evaluation, diagnosis, and treatment, so it is essential to accurately segment the orbital tumor to assist clinicians in making reasonable decisions. Nowadays, encoder-decoder-based convolutional neural networks have been widely used in medical image segmentation tasks. However, the commonly used single tensor flow architecture cannot achieve satisfactory performance for segmentation tasks with significant size variations. In this paper, we propose a size-sensitive deep network named TriBranchU-Net, which consists of a Small Branch with fewer down-sampling layers to enhance the feature learning of small regions and a Large Branch with atrous convolutional residual connections to enhance the feature learning of large regions. Then a multi-branch fusion module is designed to fuse the learned knowledge from different branches for the final segmentation. We built a large dataset for evaluation, including 602 CT images from 64 patients with orbital tumors. The experimental results show that our method can achieve superior performance in different sizes. Moreover, additional experimental results on the CVC-ClinicDB dataset further demonstrate that our TriBranchU-Net can better handle the size variation in segmentation.