Abstract: The dynamic topology of Low-orbit satellite networks is highly susceptible to node failures and link disruptions in complex environments, posing significant threats to communication system robustness. To address the limitations of traditional robustness evaluation methods in accurately characterizing network structural features and coordinating multiple optimization objectives, this paper proposes a novel topology optimization approach that integrates Graph Convolutional Networks (GCN) with a multi-objective optimization algorithm (NSGA-II), termed GCNMO. In this paper, the GCN model is first employed to capture the damage-aware features of network nodes and construct a weighted adjacency matrix, where a weighted natural connectivity metric is introduced to quantify network robustness. Then, a heuristic nearest-neighbor connection strategy is utilized to enhance the quality of the initial topology population. Finally, the NSGA-II algorithm is applied to conduct multi-objective optimization of network topologies, guiding the search toward the Pareto-optimal solution set. The simulation results show that the proposed approach significantly improves network robustness and communication performance, thereby enhancing the stability and reliability of LEO satellite networks under complex environmental conditions.