In order to investigate the microscopic characteristics between the acid medium and the sandstone, based on the digital core model and the lattice Boltzmann equation, this paper carried out an simulation test of the acid corrosion process of the sandstone, and analyzed the seepage characteristics of the sandstone under different acidic environmental circumstances. Firstly, the structural changes of the internal mineral components of the acid-corroded sandstone were studied by CT scanning equipment. Then, the seepage model of the sandstone subjected to acid corrosion was constructed by combining the digital core of acid-corroded sandstone which is established by the visual image processing software Image J, Avizo and the lattice Boltzmann theoretical equation. The change rules of the internal pore structure and seepage characteristics of sandstone in the process of acid corrosion were analyzed. Results show that the mineral composition and pore distribution of sandstone and the corrosion degree of the sandstone by acidic solution could be revealed by CT scan tests. The penetration depth increases with the increase of porosity. The rate of increase is first fast and then slow when the porosity is large, and finally tends to be stable. It indicates that the seepage model based on Boltzmann equation has good applicability for simulating the acid corrosion process of sandstone.