Because the air quality in different regions of the city are correlated with each other in both time and space, the traditional deep learning model structure is relatively simple, and it is difficult to model from the perspectives of time and space. Aiming at this problem, a Spatio Temporal Air Quality Index (STAQI) model that can simultaneously extract the complex spatial and temporal relationships between air qualities was proposed for air quality prediction. The model was composed of local components and global components, which were used to describe the influences of local pollutant concentration and air quality states of adjacent sites on the air quality prediction of target site, and the prediction results were obtained by using the weighted fusion component output. In the global component, the graph convolutional network was used to improve the input part of the gated recurrent unit network, so as to extract the spatial characteristics of the input data. Finally, STAQI model was compared with various baseline models and variant models. Among them, the Root Mean Square Error (RMSE) of STAQI model is decreased by about 19% and 16% respectively compared with those of the gated recurrent unit model and the global component variant model. The results show that STAQI model has the best prediction performance for any time window, and the prediction results of different target sites verify the strong generalization ability of the model.