A microstructure-based modeling method is developed to predict the mechanical behaviors of lithium-ion battery separators. Existing battery separator modeling methods cannot capture the structural features on the microscale. To overcome this issue, we propose an image-based microstructure Representative Volume Element (RVE) modeling method, which facilitates the understanding of the separators' complex macro mechanical behaviors from the perspective of microstructural features. A generic image processing workflow is developed to identify different phases in the microscopic image. The processed RVE image supplies microstructural information to the Finite Element Analysis (FEA). Both mechanical behavior and microstructure evolution are obtained from the simulation. The evolution of microstructure features is quantified using the stochastic microstructure characterization methods. The proposed method successfully captures the anisotropic behavior of the separator under tensile test, and provides insights into the microstructure deformation, such as the growth of voids. We apply the proposed method to a commercially available separator as the demonstration. The analysis results are validated using experimental testing results that are reported in literature.