Sleep staging is helpful in assessing sleep quality and diagnosing sleep disorders. However, how to adequately capture the temporal and spatial relations of the brain during sleep remains a challenge. In particular, existing methods cannot adaptively infer spatial-temporal relations of the brain under different sleep stages. In this paper, we propose a novel Bayesian spatial-temporal relation inference neural network, named Bayesian spatial-temporal transformer (BSTT), for sleep staging. Our model is able to adaptively infer brain spatial-temporal relations during sleep for spatial-temporal feature modeling through a well-designed Bayesian relation inference component. Meanwhile, our model also includes a spatial transformer for extracting brain spatial features and a temporal transformer for capturing temporal features. Experiments show that our BSTT outperforms state-of-the-art baselines on ISRUC and MASS datasets. In addition, the visual analysis shows that the spatial-temporal relations obtained by BSTT inference have certain interpretability for sleep staging.