The multi-satellite task scheduling problem is an optimization problem with NP-hard characteristics. Facing the growth of satellite resource scale and task demand scale, the traditional scheduling method is not efficient. In-orbit satellites have accumulated rich scheduling data during their perennial operation. Considering the large-scale multi-satellite task scheduling scenario, a multi-satellite multi-beam task scheduling model is established, and a data-driven based network predictive scheduling algorithm for multi-satellite tasks is proposed. With the idea of segmentation, task schedulability prediction in multi-satellite scenarios is realized. The designed 3 static features and 5 dynamic features are extracted from the historical scheduling data to build and train the prediction network that can be used to predict the probability of tasks being completed by different satellites, and the initial allocation scheme for tasks and resource satellites is obtained based on the principles of conflict avoidance and load balancing. We further design an evolutionary algorithm with a double-chain structure, which characterizes the above relationship. The algorithm contains evolutionary operators such as designed crossover and repair, optimizes the tasks sequence and resources allocation relationship in the initial scheme, and outputs the final task scheduling scheme. The simulation results show that, compared with the improved ant colony optimization algorithm, hybrid genetic algorithm and data-driven parallel scheduling approach, the proposed algorithm has better performance in three aspects: running time, scheme revenue and satellite load balancing.