As one of the most important applications of industrial Internet of Things, intelligent transportation system aims to improve the efficiency and safety of transportation networks. In this article, we propose a novel Bayesian framework entitled variational graph recurrent attention neural networks (VGRAN) for robust traffic forecasting. It captures time-varying road-sensor readings through dynamic graph convolution operations and is capable of learning latent variables regarding the sensor representation and traffic sequences. The proposed probabilistic method is a more flexible generative model considering the stochasticity of sensor attributes and temporal traffic correlations. Moreover, it enables efficient variational inference and faithful modeling of implicit posteriors of traffic data, which are usually irregular, spatial correlated, and multiple temporal dependents. Extensive experiments conducted on two real-world traffic datasets demonstrate that the proposed VGRAN model outperforms state-of-the-art approaches while capturing innate ambiguity of the predicted results.