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Magnetic Resonance Imaging (MRI) plays an important role in diagnosing the parotid tumor, where accurate segmentation of tumors is highly desired for determining appropriate treatment plans and avoiding unnecessary surgery. However, the task remains nontrivial and challenging due to ambiguous boundaries and various sizes of the tumor, as well as the presence of a large number of anatomical structures around the parotid gland that are similar to the tumor. To overcome these problems, we propose a novel anatomy-aware framework for automatic segmentation of parotid tumors from multimodal MRI. First, a Transformer-based multimodal fusion network PT-Net is proposed in this paper. The encoder of PT-Net extracts and fuses contextual information from three modalities of MRI from coarse to fine, to obtain cross-modality and multi-scale tumor information. The decoder stacks the feature maps of different modalities and calibrates the multimodal information using the channel attention mechanism. Second, considering that the segmentation model is prone to be disturbed by similar anatomical structures and make wrong predictions, we design anatomy-aware loss. By calculating the distance between the activation regions of the prediction segmentation and the ground truth, our loss function forces the model to distinguish similar anatomical structures with the tumor and make correct predictions. Extensive experiments with MRI scans of the parotid tumor showed that our PT-Net achieved higher segmentation accuracy than existing networks. The anatomy-aware loss outperformed state-of-the-art loss functions for parotid tumor segmentation. Our framework can potentially improve the quality of preoperative diagnosis and surgery planning of parotid tumors.