Thermal management is indispensable to the lithium-ion battery packs utilized in electrical vehicles. In this study, a novel air-cooling-based battery thermal management system with the heat fins-assisted phase change material/expanded graphite structure is proposed. After verification of the accuracy of the thermal model based on experimental measurements, numerical studies are performed on a battery submodule. All the results are obtained at an ambient temperature of 25 degrees C. Considering the complexity of the multi-physics modeling, a Kriging-based high-dimensional model representation method is employed to perform the global sensitivity analysis with relatively low computational effort. The results reveal the influence of the design variables on the thermal performance of the proposed cooling system. Moreover, this method reveals the correlations between the design variables, which reduce the dimensions of the given problem and improve the computational efficiency during optimization. Finally, a series of simulation-based tests is performed to validate the superiority of the optimal cooling system under realistic and extreme operation conditions. The comparison results show that this system can effectively improve the thermal behavior of the battery, and this cooling system after optimization provides much better cooling efficiency in alleviating the temperature increase and reducing the temperature difference of the batteries within the battery packs compared to the original one.