The development of low earth orbit (LEO) satellites has become a crucial and essential component with the advancement of digitalization. However, LEO satellites also face various security challenges within their networks, and the failure of certain satellites may trigger cascading failures. To gain a deeper understanding of cascading failure process in LEO satellite networks and enhance its robustness, this letter proposes a novel satellite network model by combining complex network and hypernetwork theories. By altering the network structure and model parameters, the robustness performance of the LEO satellite network under three types of attacks and two different load distribution methods is thoroughly investigated. The results indicate that satellite networks with varying structures are distinct and exhibit different robustness characteristics under specific attack types. Furthermore, the robustness of satellite networks in multiple attack scenarios can be significantly enhanced by implementing improved load allocation strategies. These findings not only provide a theoretical foundation for the design and optimization of satellite networks but also ignite new perspectives and ideas for future research on their robustness.