From June 2014 to January 2015, the slumped price of crude oil mainly be caused by the increasing shale gas in the U.S. The market of crude oil was altered by the variation of natural gas trade patterns. It implies that the international fossil energy trade is a multilayer structure, and each layer is a complex system with numerous countries and complicated relations. In this paper, we build the international fossil energy trade multilayer network (ETMN), and study the evolutionary characteristics of networks during 2002-2013. The generalization of several important indicators, including degree distribution, community, stability of communities and the time-varying evolution of main countries' importance were discussed. Our conclusions suggest that: Firstly, the ETMN and three energy-specific networks including coal, oil, and natural gas display the scale-free characteristic in un-weighted and weighted networks. However, it shows that even if a few countries have major trading partners, there are not always a few countries that play critical roles in trade intensity. Secondly, the natural gas network has the largest number of communities and stability compared with networks of coal and oil, and the volatility of stability lagged one year than the other two networks for the specific form of pipeline transportation. Thirdly, studying on the stability of networks shows that geopolitical environment is the most important influenced factor, but the status of renewable and new energy increases with its development obviously. Fourthly, the evolutionary characteristics of three major countries' importance, including United States, China and Japan, are analyzed in detail. At last, some policy suggestions were pointed out according to the results. (C) 2015 Elsevier Ltd. All rights reserved.