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Existing studies in few-shot semantic segmentation only focus on mining the target object information, however, often are hard to tell ambiguous regions, especially in non-target regions, which include background (BG) and Distracting Objects (DOs). To alleviate this problem, we propose a novel framework, namely Non-Target Region Eliminating (NTRE) network, to explicitly mine and eliminate BG and DO regions in the query. First, a BG Mining Module (BGMM) is proposed to extract the BG region via learning a general BG prototype. To this end, we design a BG loss to supervise the learning of BGMM only using the known target object segmentation ground truth. Then, a BG Eliminating Module and a DO Eliminating Module are proposed to successively filter out the BG and DO information from the query feature, based on which we can obtain a BG and DO-free target object segmentation result. Furthermore, we propose a prototypical contrastive learning algorithm to improve the model ability of distinguishing the target object from DOs. Extensive experiments on both PASCAL-5i and COCO-20i datasets show that our approach is effective despite its simplicity.