The structural health monitoring system (SHMS) provides an effective tool to conduct full-scale measurements on existing bridges for essential research on bridge wind engineering. In July 2008, Typhoon Fung-Wong lashed China and hit Sutong cable-stayed bridge (SCB) in China. During typhoon period, full-scale measurements were conducted to record the wind data and the structural vibration responses were collected by the SHMS installed on SCB. Based on the statistical method and the spectral analysis technique, the measured data are analyzed to obtain the typical parameters and characteristics. Furthermore, this paper analyzed the measured structural vibration responses and indicated the vibration characteristics of the stay cable and the deck, the relationship between structural vibrations and wind speed, the comparison of upstream and downstream cable vibrations, the effectiveness of cable dampers, and so forth. Considering the significance of damping ratio in vibration mitigation, the modal damping ratios of the SCB are identified based on the Hilbert-Huang transform (HHT) combined with the random decrement technique (RDT). The analysis results can be used to validate the current dynamic characteristic analysis methods, buffeting calculation methods, and wind tunnel test results of the long-span cable-stayed bridges.