Abstract: Finite element mesh size has considerable effect on theresult of optimum design when the topology optimization method based ondesign variable of element (node) is used to design structure and material.The cell should be divided into very small size grids for no-slip boundarycondition at fluid-solid interface in microstructure design of materialpermeability. Material microstructure design with inverse homogenizationmethod based on adaptive mesh is studied in this paper. The objectivefunction is maximizing isotropic permeability coefficient. The finiteelement mesh near fluid-solid interface will be refined adaptively duringoptimization iteration process for decreasing computing scale ofoptimization problem. With this algorithm, the material microstructure isobtained to be uniform from different initial density distributions. Theresult illustrates the effectiveness of our method.