With the rapid development of the global economy, air pollution, which restricts sustainable development and threatens human health, has become an important focus of environmental governance worldwide. The modeling and reliable prediction of air quality remain substantial challenges because uncertainties residing in emissions data are unknown and the dynamic processes are not well understood. A number of machine learning approaches have been used to predict air quality to help alleviate air pollution, since accurate air quality estimation may result in significant social-economic development. From this perspective, a novel air quality estimation approach is proposed, which consists of two components: newly-designed dendritic neural regression (DNR) and customized scale-free network-based differential evolution (SFDE). The DNR can adaptively utilize spatio-temporal information to capture the nonlinear correlation between observations and air pollutant concentrations. Since the landscape of the weight space in DNR is vast and multimodal, SFDE is used as the optimization algorithm due to its powerful search ability. Extensive experimental results demonstrate that the proposed approach can provide stable and reliable performances in the estimation of both PM2.5 and PM10 concentrations, being significantly better than several commonly-used machine learning algorithms, such as support vector regression and long short-term memory.