This paper presents a 3D microstructure model to predict mechanical behaviors of the anisotropic battery separator. A statistical characterization and stochastic reconstruction method is established to enable 3D microstructure modeling based on 2D microscopic images. Statistics of the key microstructure characteristics, such as porosity and the shape of the voids, are quantified by image-based characterization. Furthermore, a stochastic reconstruction algorithm is proposed to generate random but statistically equivalent 3D microstructure models for mechanical property analysis and uncertainty quantification. The proposed method is demonstrated on a commercial separator. Uniaxial tensile simulations are conducted with Finite Element Analysis (FEA) and the results are validated by experimental data. The 3D microstructure model captures anisotropic properties of the separator, and gives insights about the microstructure features under tensile load.