As air quality is closely related to human life and physical and mental health, the data of air quality has become a concern of the entire society. This study analyzes the characteristics of air quality data from a visibility graph networks point of view. The authors select eight monitoring stations in Beijing as samples. The time series of air quality data is mapped to a complex network based on the visibility graph algorithm. First, the authors study the topological structure of the networks for all the monitoring stations. Comparison results show that all constructed networks have similar structures in terms of the average path length, the network diameter, average clustering coefficient, density and the average degrees. Then the authors study the evolution of the visibility graph network for Huairou Town station for a long period of time. On the one hand, the value of the node degree indicates that the most important dates for air quality are the end of April, the beginning of May and the first three weeks of winter. On the other hand, the small-world properties of the networks reveals that the air quality data for the year 2014 is more stable without extreme fluctuations. This finding is consistent with the conclusion that air quality is largely affected by the weather while human activities play a more and more important role.