In recent years, air pollution has become increasingly serious and poses a great threat to human health. Timely and accurate air quality prediction is crucial for air pollution early warning and control. Although data-driven air quality prediction methods are promising, there are still challenges in studying spatial–temporal correlations of air pollutants to design effective predictors. To address this issue, a novel model called adaptive adjacency matrix-based graph convolutional recurrent network (AAMGCRN) is proposed in this study. The model inputs Point of Interest (POI) data and meteorological data into a fully connected neural network to learn the weights of the adjacency matrix thereby constructing the self-ringing adjacency matrix and passes the pollutant data with this matrix as input to the Graph Convolutional Network (GCN) unit. Then, the GCN unit is embedded into LSTM units to learn spatio-temporal dependencies. Furthermore, temporal features are extracted using Long Short-Term Memory network (LSTM). Finally, the outputs of these two components are merged and air quality predictions are generated through a hidden layer. To evaluate the performance of the model, we conducted multi-step predictions for the hourly concentration of PM2.5, PM10 and O3 at Fangshan, Tiantan and Dongsi monitoring stations in Beijing. The experimental results show that our method achieves better predicted effects compared with other baseline models based on deep learning. In general, we designed a novel air quality prediction method and effectively addressed the shortcomings of existing studies in learning the spatio-temporal correlations of air pollutants. This method can provide more accurate air quality predictions and is expected to provide support for public health protection and government environmental decision-making.