This study is an attempt to calculate the economic damages from 2020 to 2090 with Nordhaus's DICE model using the probabilities of global mean surface temperature changes from 2020 to 2090 under RCPs and A1B. Also, probability cumulative density curves are fitted according to the improved lognormal distribution, then probability density curves are obtained. Furthermore, we analyze the tendencies of these curves, especially the fatten tails. After that, economic damages are calculated under warming probabilities of 5%、1%、0.5% for each decade from 2020 to 2090, and effects of temperature imposed on loss rate are also analyzed. The results show that under the different scenarios of carbon emissions, the tail of the probability density curve of the global annual GDP loss rate shows a character of small probability of large loss. In conclusion, we offer more possible damage estimates in probabilistic perspective under uncertain warming events in order to provide a better understanding of risk aversion with a rapid warming world.