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Correlation filter has drawn increasing interest in visual tracking due to its high efficiency, however, it is sensitive to partial occlusion, which may result in tracking failure. To address this problem, we propose a novel local-global correlation filter (LGCF) for object tracking. Our LGCF model utilizes both local-based and global-based strategies, and effectively combines these two strategies by exploiting the relationship of circular shifts among local object parts and global target for their motion models to preserve the structure of object. In specific, our proposed model has two advantages: (1) Owing to the benefits of local-based mechanism, our method is robust to partial occlusion by leveraging visible parts. (2) Taking into account the relationship of motion models among local parts and global target, our LGCF model is able to capture the inner structure of object, which further improves its robustness to occlusion. In addition, to alleviate the issue of drift away from object, we incorporate temporal consistencies of both local parts and global target in our LGCF model. Besides, we adopt an adaptive method to accurately estimate the scale of object. Extensive experiments on OTB15 with 100 videos demonstrate that our tracking algorithm performs favorably against state-of-the-art methods.