The prediction of air quality has been a hot research topic in environmental issues. Due to the obvious regional characteristics of air pollution in Handan, the prediction of the Air Quality Composite Index (AQCI) in Handan was carried out considering the socio-economic factors in Handan and the surrounding cities. Firstly, the main factors affecting the AQCI of Handan were screened from the added value of primary industry, added value of industry, added value of construction industry, added value of tertiary industry, number of resident population and vehicle ownership in Handan and its five surrounding cities using a grey correlation analysis model. Then, considering the variability of development trends and information priorities among different city factors, a grey unequal new information priority multivariate convolution prediction model (UNGMC(1,N)) is proposed, and the particle swarm algorithm is used to adaptively optimize the nonlinear model parameters. The model comparison results show that the stability and prediction accuracy of the proposed UNGMC(1,N) model are significantly higher than those of other grey models and some popular air quality prediction methods. According to the research results, the air quality of Handan city is mainly influenced by the number of permanent residents in Handan city, and the air quality of Handan city is negatively correlated with the number of permanent residents in Handan city. In terms of regional pollution, the air quality of Handan city shows a positive correlation with the added value of tertiary industry in the neighboring city of Anyang. In addition, Handan's air quality will continue to improve in the future with U-shaped improvement efficiency and 2024 will be a critical year for Handan's air quality improvement efficiency.