The microscopic pore structure of sandstone determines its macroscopic permeability. Based on computer tomography (CT) technology, CT scans were performed on three different types of sandstone pore structures, namely coarse sandstone, medium sandstone, and fine sandstone. And the three-dimensional microscopic structure of sandstone pores was reconstructed. Furthermore, based on the Navier–Stokes equations, the fluid flow process in the pore structure of sandstone was simulated, and the effective permeability of sandstone was obtained. By extracting the pore structure from sandstone CT images, the average porosity of coarse sandstone, medium sandstone, and fine sandstone was 16.43%, 12.03%, and 11.64%, respectively. And the porosity of unconnected pores is less than 0.5%. The porosity and permeability of coarse sandstone are higher than those of medium sandstone and fine sandstone with an average value of 1.7 D. The porosity of medium sandstone and fine sandstone is relatively similar. However, the average pore radius and pore throat radius of medium sandstone are larger than those of fine sandstone. More importantly, although the permeability and porosity of sandstone are generally linearly related, when the porosity is low, the data show a large dispersion, and auxiliary indicators such as pore structure characteristic parameters such as pore throat radius should be adopted to evaluate the permeability of sandstone. The flow trajectory of fluid in the pore structure of sandstone is revealed through the streamline of fluid in the pore structure, revealing the mechanism of fluid flow.