Fractures greatly influence fluid flow and mass transport in projects of radioactive waste disposal in deep geological formations. This work investigates the mechanism of nuclide migration in fractured rocks by considering fracture roughness based on a unified pipe-network method (UPM). The processes of adsorption and decay are incorporated into the UPM framework to capture the nuclide migration in a rock mass with rough-walled fracture networks. Benchmark tests are attempted against analytical results of the concentration distribution along a single fracture. An equivalent method to approach the hydraulic fracture aperture in fractured rocks by considering fracture roughness is also demonstrated. The influences of the distribution of fracture roughness, the rock matrix adsorption capacity, and the transport properties on the process of nuclide migration are investigated. The breakthrough curve for the nuclide migration moves toward a longer time with increasing fracture roughness. The increased diffusion coefficient and retardation factor in the rock matrix greatly enhance the matrix retardation effect on nuclide migration. Furthermore, the nuclide featuring a longer half-life results in a higher relative nuclide concentration in the domain. A hydraulic gradient with a relatively low value greatly impacts the distribution of the relative concentration.