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Automatic and accurate tumor segmentation on medical images is in high demand to assist physicians with diagnosis and treatment. However, it is difficult to obtain massive amounts of annotated training data required by the deep-learning models as the manual delineation process is often tedious and expertise required. Although self-supervised learning (SSL) scheme has been widely adopted to address this problem, most SSL methods focus only on global structure information, ignoring the key distinguishing features of tumor regions: local intensity variation and large size distribution. In this paper, we propose Scale-Aware Restoration (SAR), a SSL method for 3D tumor segmentation. Specifically, a novel proxy task, i.e. scale discrimination, is formulated to pre-train the 3D neural network combined with the self-restoration task. Thus, the pre-trained model learns multi-level local representations through multi-scale inputs. Moreover, an adversarial learning module is further introduced to learn modality invariant representations from multiple unlabeled source datasets. We demonstrate the effectiveness of our methods on two downstream tasks: i) Brain tumor segmentation, ii) Pancreas tumor segmentation. Compared with the state-of-the-art 3D SSL methods, our proposed approach can significantly improve the segmentation accuracy. Besides, we analyze its advantages from multiple perspectives such as data efficiency, performance, and convergence speed.