Climate risk is one of the key factors affecting the energy industry, and then affects the global energy trade. By adopting a network approach to the global energy trade and based on the data of global energy trade during 1996-2018, the evolution characteristics of the global energy trade network are hereby investigated, and the impact of climate risk on the global energy trade is explored. The results demonstrate that the global energy trade network has scale-free characteristics and significant regional characteristics and that its heterogeneity is weakening on the whole. Climate risk is negatively correlated with the energy trade relationship between countries. The simulation results show that climate risk has a greater impact on the import status of all countries than their export status and that only a few countries have large climate risk spillover effects. In addition, the climate risk spillover effects of countries are closely related to their import statuses. Overall, the present study provides policy suggestions for identifying important energy trading countries under climate risk shock and preventing the negative impact of climate risks on global energy trade.