Concrete inevitably contains microcracks, but their significance on transport properties and long-term durability is not well established. This is because of difficulties in isolating and evaluating the effect of microcracks whether by laboratory experiments or computer simulations, owing to their complex heterogeneous nature. In this paper, a three-dimensional numerical approach to simulate mass transport properties of concrete containing microcracks is presented. The approach is based on finite-element method and adopts aligned meshing to improve computational efficiency. The mesostructure of concrete is represented by aggregate particles that are surface meshed by triangulation and porous cement paste matrix that are discretised with tetrahedral elements. Microcracks are incorporated as interface elements at the aggregate-paste interface or at the cement paste matrix spanning neighbouring aggregate particles. The main advantage of this approach is that the smallest microcracks can be simulated independent of the discretisation size. The model was first validated by comparing the simulations to available analytical solutions. Then, the diffusivity and permeability of a range of concretes containing different amounts of microcracking with increasing complexities were simulated. The results are analysed and discussed in terms of the effect of microcrack type (bond, matrix), volume fraction, width, specific surface area and degree of percolation on transport properties.