Low Earth Orbit (LEO) satellite networks are inexpensive to deploy and have wide coverage, and are widely available for differentiated content distribution services. With the development of on-board storage and computing capabilities, in-network caching technology in information centric networking (ICN) has proven to be an effective way to increase the throughput and content distribution efficiency of satellite networks. However, traditional caching and distribution schemes, which do not take into account the high-speed motion of satellite nodes and dynamic changes in topology, are not applicable to satellite networks. To address these issues, a hybrid caching strategy for satellite networks based on node classification and popular content awareness (NCPCA) is proposed. Firstly, the time slot partitioning method based on interlayer similarity is proposed to transform the dynamically changing process into a set of time slots with stable topology. Next, the satellite nodes are dynamically divided into two categories by fully considering the changes in connection relationships and interaction order during the spatial–temporal evolution of the satellite nodes. Nodes with satellite topological and functional characteristics are screened out as core nodes with TOPSIS algorithm, and the remaining nodes are regarded as edge nodes. Finally, a probabilistic caching scheme based on content popularity is adopted with core nodes as caching nodes to ensure caching performance and promote the diversity of cached content. Simulation results show that this strategy can effectively improve cache hit rate, reduce user request delay and content fetching hops, and promote the stable operation of satellite networks compared with other caching strategies.