Satellite scheduling problems (SSP) are NP-Hard combinatorial optimization problems and have been widely studied in the field of aerospace engineering. Traditional methods for solving SSPs, such as heuristic algorithms and mixed-integer linear programming, are highly dependent on expert experience and are not easily generalized. In recent years, some methods based on end-to-end deep reinforcement learning (DRL) has been proposed to solve SSPs, but they often lack robustness and interpretability for more challenging problems. In this study, we propose a hybrid satellite scheduling method that combines local search (LS) with DRL. The method uses LS as the primary problem-solving framework and allows the DRL agent to assist in decision-making for the iterative search strategy of the solution. In our method, the SSP instance is modeled as a near-bipartite graph, based on which the LS algorithm is designed. The DRL network architecture is based on Graph Convolutional Networks (GCN), and the problem’s graph model is simplified to reduce the complexity and computational overhead of the neural network. Our hybrid algorithm is tested on four problem instances of varying sizes and difficulty levels, and the results show that it can achieve better performance than the original pure LS method, with a significant reduction in the number of search iterations required to find the optimal solution.