Understanding the fluid flow and solute transport mechanisms in fractured rocks is essential for many geo-engineering applications. In this study, the fluid flow and solute transport in a fracture-matrix system with a three-dimensional (3-D) discrete fracture network (DFN) are modelled through an efficient numerical simulation workflow. The simulation approach is used to systematically investigate the effects of the rock matrix on the transport behaviors in a fracture-matrix system. The results show that the mass exchange between the DFN and the rock matrix can be accurately evaluated based on the conforming mesh at the interface between the fractures (using triangular elements) and the rock matrix (using tetrahedral elements). The complementary cumulative distribution function curves (CCDFs) for the physical processes that consider sorption and decay exhibit significant long tail characteristics, which suggests that the sorption and decay processes play an important role in retarding the migration of solutes in fractured rocks. It is also found that a larger matrix porosity enhances the mass exchange at the interface between the DFN and the rock matrix, which consequently promotes the matrix diffusion effects. The distribution of the concentration plumes in the matrix demonstrates in fracture-matrix systems with larger fracture densities could result in a better connection between the fracture networks and the larger interface (specific wetting) areas, which therefore, promotes the mass exchange. These findings are critical to understanding the migration behavior of radioactive nuclides in far field areas and for the deep geological disposal of nuclear waste.