Abstract Tracking by siamese networks has achieved favorable performance in recent years. However, most of existing siamese methods do not take full advantage of spatialtemporal target appearance modeling under different contextual situations. In fact, the spatial-temporal information can provide diverse features to enhance the target representation, and the context information is important for online adaption of target localization. To comprehensively leverage the spatial-temporal structure of historical target exemplars and get benefit from the context information, in this work, we present a novel Graph Convolutional Tracking (GCT) method for high-performance visual tracking. Specifically, the GCT jointly incorporates two types of Graph Convolutional Networks (GCNs) into a siamese framework for target appearance modeling. Here, we adopt a spatial-temporal GCN to model the structured representation of historical target exemplars. Furthermore, a context GCN is designed to utilize the context of the current frame to learn adaptive features for target localization. Extensive results on 4 challenging benchmarks show that our GCT method performs favorably against state-of-the-art trackers while running around 50 frames per second.