It is of great significance to analyze the invulnerability of electric power backbone communication network for evaluating the survivability of electric power communication network and formulating network protection strategies. Based on the heterogeneity of complex networks and the topological structure of electric power backbone communication network, the network node difference matrix is constructed. According to the characteristics of power communication services, the network link difference matrix is constructed with regarding the link traffic as the link weight. Combining the differences of nodes and links, the importance of nodes and the structural entropy of electric power backbone communication network are defined. For a practical network, the simulation analysis of node importance and network invulnerability under intentional attack based on structural entropy is carried out, and the results show that the method proposed in this paper is more accurate and effective for electric power backbone communication network than other comparative methods. This work is supported by Science and Technology Project of State Grid Corporation of China (No. 5700- 201919238A-0-0-00) and Science and Technology Project of State Grid Gansu Provincial Electric Power Company (No. 271833-KXKJ-034).