Low Earth Orbit (LEO) satellites offer short response times and wide coverage for tracking time-sensitive moving targets. However, when multiple satellites work together, planning and scheduling become challenging because observation resources are limited and target states change over time. The widely used Consensus-Based Bundle Algorithm (CBBA) typically relies on a greedy utility rule, which can lead to uneven allocation and suboptimal overall performance. To address this, we introduce the Shapley value from cooperative game theory into CBBA to score each agent’s marginal contribution within a coalition, replacing the greedy utility function. This change helps balance individual satellite gains with system-level objectives during task assignment. For time-sensitive tasks, we develop a multi-satellite cooperative planning and scheduling model and design an improved CBBA–Shapley workflow. In simulations involving continuous tracking of maneuvering targets by an LEO constellation, the proposed method outperforms standard CBBA in mission completion rate, fairness, and overall utility. Under tight resource conditions, it also shows stronger scheduling robustness and a closer approach to global optimality. These results provide an effective optimization strategy for cooperative scheduling of LEO satellite systems in time-sensitive missions.