With the establishment of China’s national air quality monitoring network, large amounts of monitoring data are available for different kinds of users. How to process and use this big data is a tough problem for users: most users have limited computing power, and new data are collected at every moment. Cloud computing may be an efficient and low-cost way to solve this problem. This paper investigates a problem of a complex system: the impact of PM2.5 on hospitalization for respiratory diseases. A change-point detection method based on grey relation analysis was used to solve this problem. Daily air pollution monitoring data and patient data were used in this study. Our results showed that (1) PM2.5 pollution showed a positive correlation on hospital admission for respiratory disease; (2) most patients went to hospital 2 days after PM2.5 pollution events; and (3) male, children, and old people were significantly affected by PM2.5 pollution. Our study is of great significance to help the government formulate suitable policies to reduce the damage caused by PM2.5 pollution and help hospitals allocate medical resources efficiently.