Abstract: As the proportion of natural gas consumption in the energy market gradually increases, optimizing the design of gas storage surface system (GSSS) has become a current research focus. Existing studies on the two independent injection pipeline network (InNET) and production pipeline network (ProNET) for underground natural gas storage (UNGS) are scarce, and no optimization methods have been proposed yet. Therefore, this paper focuses on the flow and pressure boundary characteristics of the GSSS. It constructs systematic models, including the injection multi-condition coupled model (INM model), production multi-condition coupled model (PRM model), injection single condition model (INS model) and production single condition model (PRS model) to optimize the design parameters. Additionally, this paper proposes a hybrid genetic algorithm based on generalized reduced gradient (HGA-GRG) for solving the models. The models and algorithm are applied to a case study with the objective of minimizing the cost of the pipeline network. For the GSSS, nine different condition scenarios are considered, and iterative process analysis and sensitivity analysis of these scenarios are conducted. Moreover, simulation scenarios are set up to verify the applicability of different scenarios to the boundaries. The research results show that the cost of the InNET considering the coupled pressure boundary is 64.4890 × 104 CNY, and the cost of the ProNET considering coupled flow and pressure boundaries is 87.7655 × 104 CNY, demonstrating greater applicability and economy than those considering only one or two types of conditions. The algorithms and models proposed in this paper provide an effective means for the design of parameters for GSSS.