The miscible displacement with fluid-solid dissolution reaction in porous media is a typical process in many industrial applications, such as underground-water pollution decontamination, oil recovery or geological sequestration of carbon dioxide, etc. It is a significant problem in engineering and physics applications. It can be known that the dissolution reaction can change the structure of the porous media, which will have a great influence on the miscible displacement process. However, the relationship between the displacement process and the dissolution reaction in porous media is not fully studied. In this paper, the miscible displacement with dissolution in the porous media is simulated by a lattice Boltzmann method (LBM). The study focuses on the influence of the internal structure change in the displacement process, and further quantitatively analyzes the changes of the porosity and displacement efficiency by changing the Damkohler number (Da) and the Pèlcet number (Pe). The results show that when Da is large enough, the dissolution reaction will generate a few wormholes in the porous media, and the displacement fluid will leave the porous medium along the wormholes, resulting in the decrease of the displacement efficiency. As Da increases, the reaction goes faster, the rate of change in porosity increases, the wormholes become wider, does yield a larger displacement efficiency. With the increase of Pe, the fingerings develop faster, the rate of change in porosity decreases, the displacement efficiency decreases.