Tracking by siamese networks has achieved favorable performance in recent years. However, most of existing siamese methods do not take full advantage of spatial-temporal 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.