Natural gas is considered a transitional energy source in the transition to clean energy owing to its clean, efficient, and ecologically beneficial properties. The trade of liquefied natural gas (LNG) serves as the backbone of the global natural gas trade and significantly influences the dynamics of the global energy trade system. This paper constructs long-term global LNG trade networks, and explores the spatiotemporal evolution and topological structures of the international LNG trade by utilizing multilevel network analysis methods, to provide insights for comprehensively understanding the market dynamics of the global LNG trade system. The findings indicate the following: (1) The global LNG trade volume shows an overall upward trend, and the global LNG trade network exhibits uneven spatial distribution, clear hierarchical differentiation, and an increasingly complicated structure. Global LNG trade is gradually changing from regionalization to globalization, and the international LNG market is undergoing structural reshaping. (2) The global LNG trade network continues to expand in size and density, and the rapidly growing LNG supply and trade relations are driving the formation of the global natural gas market. (3) Global LNG trade is still in a phase of rapid change, with the global efficiency of the network increasing and then decreasing. The trade network has traditionally been centered on ten countries, including Japan, South Korea, the United States, and Qatar. (4) The global LNG trade network exhibits clear core-periphery structures with considerable polarization effects, and the trade network structure is continuously evolving and is growing unbalanced. Finally, we put forward relevant policy suggestions to promote global LNG trade interconnectivity and enhance environmental protection and respond to global climate change.