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To improve the ability of responding to emergencies in the scheduling of relay satellite system, a dynamic scheduling model is proposed based on the rolling horizon strategy in this paper, which decomposes the complex dynamic scheduling process into several static scheduling subproblems. A multi-objective optimization algorithm is designed to solve the subproblems according to the demand for dynamic scheduling of the relay satellite. Firstly, a dynamic scheduling model for the relay satellite is constructed to obtain the maximum task completion rate and the minimum adjustment range of scheduling scheme. Then, based on dynamic scheduling characteristics, a dynamic task scheduling method is proposed. The method adopts a hybrid rescheduling mechanism based on cycle and event-driven, divides the scheduling process into scheduling intervals, and uses a multi-objective evolutionary algorithm based on adaptive neighborhood search to schedule the window tasks in each interval. To verify the effectiveness of the proposed dynamic scheduling model and algorithm, a large number of simulation experiments are carried out. The experimental results prove the superiority of the proposed method in solving the dynamic scheduling problem of relay satellite. Compared with the cutting-edge multi-objective optimization methods of NSGA-Ⅱ, MDSA-NSGA-Ⅱ, and MODJA, the algorithm designed in this paper can generate higher quality solutions.