Owing to the harsh environment, the support conditions of wind turbines inevitably degrade/change over their lifetime, however, the evolution mechanism is not yet well understood. Although the damping parameters are sensitive to structural support and connection conditions, they are difficult to measure and quantify, which is a challenging inverse problem. This study aims to develop an approach to obtain a statistical time-domain damping parameter (STDP) based on operational vibration signals, and to utilize the parameter to identify support conditions of wind turbines. The proposed approach transforms operational vibration signals to free vibration signals by using the random decrement technique and then performs nonparametric statistical analysis to quantify the statistically significant changes in the damping characteristics of a structure. The effectiveness of the STDP method is verified by two challenging cases of bolted connection damage and soil-structure interaction condition changes. The regression analysis demonstrates the ability of the STDP method for the identification of structural overall damping. In contrast with classic modal analysis methods, the proposed method provides a monotonic relationship between the STDP and support conditions, which is significant for structural condition identification.