Low Earth Orbit satellite communication has become an important part of the integrated network between earth and space, offering low-latency, seamless communication services that are available everywhere. Adopting a Model-Based Systems Engineering approach to digital design has grown in importance as a way to deal with the complexity of such a system and increase the effectiveness of system design. The paper presents the initial design of the LEO satellite communication system architecture and demonstrates how MBSE, using the System Modeling Language (SysML), can better comprehend and analyze the system's functionality and architecture, meet stakeholder requirements, and extend the model results to the full lifecycle of system development. MBSE-based development improves the model's consistency and reusability. Based on the analysis of the requirements of the LEO access network, bearer network, and core network, the design methods and ideas of models, including the core element model refinement, communication scenario use case and activity design, satellite communication payload logical architecture design, and SysML model integration simulation analysis. The results of these models can provide support for the architecture design and key technology verification of the LEO satellite communication system.