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The environment and development are major issues of general concern. After much suffering from the harm of environmental pollution, human beings began to pay attention to environmental protection and started to carry out pollutant prediction research. A large number of air pollutant predictions have tried to predict pollutants by revealing their evolution patterns, emphasizing the fitting analysis of time series but ignoring the spatial transmission effect of adjacent areas, leading to low prediction accuracy. To solve this problem, we propose a time series prediction network with the self-optimization ability of a spatio-temporal graph neural network (BGGRU) to mine the changing pattern of the time series and the spatial propagation effect. The proposed network includes spatial and temporal modules. The spatial module uses a graph sampling and aggregation network (GraphSAGE) in order to extract the spatial information of the data. The temporal module uses a Bayesian graph gated recurrent unit (BGraphGRU), which applies a graph network to the gated recurrent unit (GRU) so as to fit the data’s temporal information. In addition, this study used Bayesian optimization to solve the problem of the model’s inaccuracy caused by inappropriate hyperparameters of the model. The high accuracy of the proposed method was verified by the actual PM2.5 data of Beijing, China, which provided an effective method for predicting the PM2.5 concentration.