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The design and construction of metro networks are typically conducted in stages due to the ongoing growth of urbanization and investment in public transportation systems. Designing new metro lines within an existing metro network is challenging as passenger flow patterns will be significantly updated and change. This study investigates new line designing in an existing metro network, also known as the metro network expansion design problem, and develops two optimization models to maximize the origin-destination (OD) demand capture under a limited budget. The first is a deterministic binary integer linear programming model, while the second is a robust optimization model that considers the demand uncertainty. The paper proposes a section-based modeling strategy to make the issue tractable and consider mode competition with other transport modes to capture the attracted demand by new metro lines. The models are applied to a real-world case in Wuxi, China, to validate their applicability and computational efficiency. The results showed satisfactory metro network expansion patterns with good connections between new lines and existing networks. The deterministic model can identify corridors and sections with higher priorities under tight budget conditions. A sensitivity analysis indicates that passengers' concerns about travel time and fares are conducive to constructing the metro network. Furthermore, the advantage of the robust solution becomes critical as the demand variation increases. The robust optimization model can provide a more reliable and competitive solution than the deterministic model under large demand variation scenarios. [ABSTRACT FROM AUTHOR]