The miscible displacement with fluid-solid dissolution reaction in a porous medium is a typical process in many industrial applications, such as underground-water pollution decontamination, and oil recovery or geological sequestration of carbon dioxide. It is a significant problem in engineering and physics applications. As is well known, the dissolution reaction can change the structure of the porous medium, which will have a great influence on the miscible displacement process. However, the relationship between the displacement process and the dissolution reaction in a porous medium has not been fully studied. In this study, the miscible displacement with dissolution in a porous medium is simulated by a lattice Boltzmann method (LBM). The study focuses on the influence of the internal structure change on the displacement process, and the further quantitative analyzing of 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 medium, 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, and the wormholes become wider, thereby indeed yielding a larger displacement efficiency. With the increase of Pe, the fingerings develop faster, the rate of change in porosity decreases, and the displacement efficiency decreases as well.