In this paper, the representative sandstone matrix and fracture sample are selected for CT scanning to build the corresponding matrix and fracture digital rock respectively. Then, based on the matrix and fracture digital rock with the same physical size and resolution, the Boolean superposition algorithm is introduced to construct matrix-fracture dual media digital rock; meanwhile, an image opening algorithm is used to eliminate pore voxel, and matrix digital rock with different micropore size is reconstructed, also, the superposition algorithm is conducted to reconstruct matrix-fracture dual digital rock with different micropore sizes. Finally, based on the matrix digital rock and matrix-fracture digital rock with different micropore sizs, the total porosity, connected porosity and absolute permeability are calculated. It can be found that, the micro pore-throat has lower contribution to the total porosity of matrix and dual media; the micropore-throat contributes more to the connected porosity of the matrix, but less to the connected porosity of dual media; the micropore-throat makes important contribution to the permeability of matrix, but less to the permeability of dual media. This paper provides an important platform to study the porosity and permeability characteristics of matrix-fracture dual media, which is of great significance to the development of dual-media reservoirs.