The layout of cable-net in air-supported membrane structures significantly affects the overall mechanical performance and economic efficiency. An optimal cable-net layout is crucial for enhancing the comprehensive performance of air-supported membrane structures. Combining the practical engineering requirements, designing a cable-net layout that satisfies both structural performance and low-carbon economy is a complex multi-objective optimization problem. Aiming at this problem, this study investigates the influences of geometric dimensions, physical parameters, and cable net layout on the structural deformation, internal forces of cables and membranes, and carbon emissions, and establishes a multi-objective optimization function. Based on a neural network model, the optimal cable-net layout is derived under the condition of minimizing the multi-objective function. Finite element model validation demonstrates that the cable-net layout obtained by the proposed multi-objective optimization neural network model ensures excellent mechanical performance and economic efficiency for air-supported membrane structures. This study provides a efficient and low-carbon optimization solution for cable-net layout in air-supported membrane structures, providing practical significance for engineering applications.