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In recent years, large‐scale satellite networks have been studied emphatically due to its advantages in high throughput and low latency. Many companies and institutions are keen to build large‐scale low earth orbit satellite constellations to provide space‐based Internet services, which poses a great demand for the design of efficient and reliable routing schemes. Three attribute indexes to evaluate the performance of the satellites are proposed. With the Dempster–Shafer theory, the attributes can be fused for the routing decision‐making process. Based on the Message Identification divergence (M‐I divergence) measure method, a Belief Message Importance divergence based Routing algorithm is proposed. By adjusting the characteristic parameter, it can amplify the divergence between distance‐based evidence and others properly. In this way, Belief Message Importance divergence‐based Routing attempts to find the optimal shortest path according to the status of intermediate nodes. Compared with existing satellite routing schemes, the algorithm that is proposed can approach the optimal routing performance, increasing the throughput by 47.2% on average, and decreasing the total delay and packet drop rate by 59.5% and 42.1% on average, respectively. [ABSTRACT FROM AUTHOR]