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Existing visual object tracking usually learns a bounding-box based template to match the targets across frames, which cannot accurately learn a pixel-wise representation, thereby being limited in handling severe appearance variations. To address these issues, much effort has been made on segmentation-based tracking, which learns a pixel-wise object-aware template and can achieve higher accuracy than bounding-box template based tracking. However, existing segmentation-based trackers are ineffective in learning the spatio-temporal correspondence across frames due to no use of the rich temporal information. To overcome this issue, this paper presents a novel segmentation-based tracking architecture, which is equipped with a spatio-appearance memory network to learn accurate spatio-temporal correspondence. Among it, an appearance memory network explores spatio-temporal non-local similarity to learn the dense correspondence between the segmentation mask and the current frame. Meanwhile, a spatial memory network is modeled as discriminative correlation filter to learn the mapping between feature map and spatial map. The appearance memory network helps to filter out the noisy samples in the spatial memory network while the latter provides the former with more accurate target geometrical center. This mutual promotion greatly boosts the tracking performance. Without bells and whistles, our simple-yet-effective tracking architecture sets new state-of-the-arts on the VOT2016, VOT2018, VOT2019, GOT-10K, TrackingNet, and VOT2020 benchmarks, respectively. Besides, our tracker outperforms the leading segmentation-based trackers SiamMask and D3S on two video object segmentation benchmarks DAVIS16 and DAVIS17 by a large margin. The source codes can be found at https://github.com/phiphiphi31/DMB.