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Traffic accident anticipation aims to predict accidents from dashcam videos as early as possible, which is critical to safety-guaranteed self-driving systems. With cluttered traffic scenes and limited visual cues, it is of great challenge to predict how long there will be an accident from early observed frames. Most existing approaches are developed to learn features of accident-relevant agents for accident anticipation, while ignoring the features of their spatial and temporal relations. Besides, current deterministic deep neural networks could be overconfident in false predictions, leading to high risk of traffic accidents caused by self-driving systems. In this paper, we propose an uncertainty-based accident anticipation model with spatio-temporal relational learning. It sequentially predicts the probability of traffic accident occurrence with dashcam videos. Specifically, we propose to take advantage of graph convolution and recurrent networks for relational feature learning, and leverage Bayesian neural networks to address the intrinsic variability of latent relational representations. The derived uncertainty-based ranking loss is found to significantly boost model performance by improving the quality of relational features. In addition, we collect a new Car Crash Dataset (CCD) for traffic accident anticipation which contains environmental attributes and accident reasons annotations. Experimental results on both public and the newly-compiled datasets show state-of-the-art performance of our model. Our code and CCD dataset are available at https://github.com/Cogito2012/UString.