Accurate and reliable air quality forecasts are essential for informed decision-making in urban planning and environmental engineering. However, predicting air quality faces challenges due to significant fluctuations in data, including the impact of extreme weather. To improve the precision of air quality predictions, it is important to account for the long- and short-term temporal dependencies within historical data from stations, as well as the local and global spatial structures among different stations in a specific region. In this paper, we propose a novel uncertainty graph convolution recurrent neural network for air quality forecasting (AirNN). Concretely, we design an uncertainty-guided graph convolution module to enhance the robustness of air quality forecasting. It treats the parameters on each graph convolution layer as probability distributions and employs variational inference to derive optimal estimates for these distributions. In addition, to capture the global correlation of stations in the whole region, we develop a spatial information modulator. It captures the spatial correlation between long-range stations in graph data. Extensive experiments on different real-world datasets demonstrate the proposed AirNN performs favorably against state-of-the-art methods. Especially in the 24-hour prediction, AirNN reduced the root mean square error (RMSE) by 0.5 on two real datasets, indicating that our proposed AirNN exhibits good performance in long-term forecasting.