Obtaining a comprehensive understanding of solute transport in fractured rocks is crucial for various geoengineering applications, including waste disposal and construction of geo-energy infrastructure. It was realized that solute transport in fractured rocks is controlled by stochastic discrete fracture-matrix systems. However, the impacts and specific uncertainty caused by fracture network structures on solute transport in discrete fracture-matrix systems have yet not been fully understood. In this article, we aim to investigate the influence of fracture network structure on solute transport in stochastic discrete fracture-matrix systems. The fluid flow and solute transport are simulated using a three-dimensional discrete fracture matrix model with considering various values of fracture density and size (i.e., radius). The obtained results reveal that as the fracture density or minimum fracture radius increases, the corresponding fluid flow and solute transport channels increase, and the solute concentration distribution range expands in the matrix. This phenomenon, attributed to the enhanced connectivity of the fracture network, leads to a rise in the effluent solute concentration mean value from 0.422 to 0.704, or from 0.496 to 0.689. Furthermore, when solute transport reached a steady state, the coefficient of variation of effluent concentration decreases with the increasing fracture density or minimum fracture radius in different scenarios, indicating an improvement in the homogeneity of solute transport results. The presented analysis results of solute transport in stochastic discrete fracture-matrix systems can be helpful for uncertainty management in the geological disposal of high-level radioactive waste.