The research of rock properties based on its inherent microscopic to mesoscopic porous structure has drawn great attention for its potential in predicting the macroscopic behavior of rocks. An accurate reconstruction of the three-dimensional porous structure is a premise for the related studies of hydraulic and mechanical properties of rocks, such as the transport properties and mechanical responses under pressures. In this paper, we present a computer procedure for reconstructing the 3D porous structure of low-permeability sandstone. Two large-size 3D models are reconstructed based on the information of a reference model which is established from computed tomography (CT) images. A self-developed finite element method is applied to analyze the nonlinear mechanical behavior of the sandstone based on its reconstructed model and to compare the results with those based on the reference model. The good consistency of the obtained mechanical responses indicates the potential of using reconstruction models to predict the influences of porous structure on the mechanical properties of low-permeability sandstone.