Different quality, reserves and production force countries to import fossil fuels to advance their economic development. It is exergy of fossil fuels that is essentially important to economy. Thus, it forms an international exergy flow network embodied in the global fossil energy trade. Based on complex network theory, we built a global fossil energy exergy flow network with countries as nodes, the international exergy flows as edges and the exergy of each flow as the weight of the edges. We analyzed the distribution of countries, the overall structure, major countries and major exergy flow paths of the network from 1996 to 2012. The results show that even if the fossil energy trade becomes more frequent and larger, there are always a few trade relationships and countries that play critical roles in the fossil energy trade. The trade relationship intensity at the global level is relatively lower than the corresponding intensity at the regional level. There are four main fossil energy trade groups, and these groups have the Russian Federation, the United States, Japan and Saudi Arabia as their core countries. If an energy war, an energy crisis or other problems occur in the countries with more partners, their impacts are likely to spread to other countries and even affect the global fossil energy trade. (C) 2015 Elsevier Ltd. All rights reserved.