In contrast to terrestrial networks, the rapid movement of low-earth-orbit (LEO) satellites causes frequent changes in the topology of intersatellite links (ISLs), resulting in dynamic shifts in transmission paths and fluctuations in multi-hop latency. Moreover, limited onboard resources such as buffer capacity and bandwidth competition contribute to the instability of these links. As a result, providing reliable quality of service (QoS) for time-sensitive flows (TSFs) in LEO satellite networks becomes a challenging task. Traditional terrestrial time-sensitive networking methods, which depend on fixed paths and static priority scheduling, are ill-equipped to handle the dynamic nature and resource constraints typical of satellite environments. This often leads to congestion, packet loss, and excessive latency, especially for high-priority TSFs. This study addresses the primary challenges faced by time-sensitive satellite networks and introduces a management framework based on software-defined networking (SDN) tailored for LEO satellites. An advanced queue management and scheduling system, influenced by terrestrial time-sensitive networking approaches, is developed. By incorporating differentiated forwarding strategies and priority-based classification, the proposed method improves the efficiency of transmitting time-sensitive traffic at multiple levels. To assess the scheme’s performance, simulations under various workloads are conducted, and the results reveal that it significantly boosts network throughput, reduces packet loss, and maintains low latency, thus optimizing the performance of time-sensitive traffic in LEO satellite networks.