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The social cost of carbon (SCC) represents monetary value of the damage caused by carbon dioxide emissions in climate change. It is an important standard for the formulation of climate policy. The uncertainty of carbon social cost is closely related to climate sensitivity, damage parameters, discount rate and so on. Previous studies have mainly focused on the consequences of climate change and the effect of social cost of carbon and welfare under different policies. Its research on the social cost of carbon has not included the evolution coefficient of carbon emissions, and it has rarely introduced the climate disaster damage function into the process of solving the social cost of carbon. This paper provides a simplified formula for the social cost of carbon. The model has a nonlinear processing of the carbon circulation system, which increases the nonlinear structure of CO2 emission potential. In addition, the model modifies the climate damage function, which adds additional losses from climate catastrophes. This paper analyzes the combined effects of several key sensitivity parameters, resulting in a "fat tail" distribution of social cost of carbon ultimately. It is found that the mean SCC of 2015 is 44.93 (sic)/tCO2 and the median SCC is 15.9054 (sic)/tCO2. Considering the possibility of extreme results and the impact of disaster risk loss on uncertain structure, the joint effects of damage parameters, climate sensitive parameters, and discount rates make the social cost of carbon as much as 2.8 times the median and fat tail effect is obvious. This brings uncertainty to the current emission reduction policies and abatement costs, making it more difficult to assess cost-effectiveness. At last, the paper evaluates the social cost of carbon under the base situation and low discount rate in China. (C) 2018 Elsevier Ltd. All rights reserved.