The soil damping, which shows an obvious relationship with the foundation type and soil parameters, has a very important effect on the dynamic response and fatigue characteristics of Offshore Wind Turbine (OWT) structure. Known as a novel type of foundation, the Wide-Shallow Bucket Foundation (WSBF) has been gradually applied in a few Offshore Wind Farms (OWF) of China during the past five years. Due to the shallow bucket skirt and the more contact area between soil and foundation, the soil damping of the OWTs supported by WSBF may reflect different foundation-soil interaction characteristics compared with monopile and jacket foundation. There, the calculation of soil damping for the OWTs supported by WSBF was focused on and discussed in this paper. Firstly, the rotation and swing theoretical model of OWT supported by WSBF was established and then the theoretical model of natural frequency calculation was also presented based on the transfer matrix method. Further, one new theoretical calculation method of soil damping for the OWT supported by WSBF was proposed considering soil hysteresis characteristics. Secondly, taking an OWT of one actual OWF as the research object, accurate theoretical estimation of soil damping for WSBF was achieved combined prototype observation, modal frequency identification and Genetic Algorithm (GA) with a value around 0.120%. Then, three different geological conditions and soil parameters of another actual OWF were selected to complete the comparison between the results obtained from the proposed theoretical calculation method and numerical simulation method, and verify the general applicability of the new model and method based on the engineering error within 5%. Finally, the influence on the soil damping of OWT structure considering different factors (compression modulus and Plasticity Index (PI)) was discussed by using the new theoretical calculation method. It is concluded that the soil damping rises with the increase of the compression modulus, while it decreases as the PI increases.