Natural discontinuities are the major concern when considering mass transport in engineered barrier systems and their host rocks. Numerical simulations of highly fractured geological formations are limited because of the contradiction between results accuracy and computational costs. To alleviate such a contradiction, this study proposes an improved fracture continuum method to simulate the radioactive spreading in a complex 3-D fracture system. With Boolean operations and the unified pipe-network method, discontinuities are mapped on structured subdomains and standardized to equivalent paths. Moreover, adaptive mesh refinement is utilized to ease the complexity further. We verify the accuracy of this method in two metric cases, and results show that perfect agreement is achieved with analytical solutions. This method demonstrates its applicability to the simulation of a nuclear leak in a repository for high-level radioactive waste. Effects of the maximum refinement level are discussed. For a room-scale problem, flow rates and mass fluxes on boundary surface converge to stable values when the maximum refinement level is larger than 4. An extensive case with complex fracture networks is modeled and compared with the conventional finite-difference method. The proposed method is capable of conducting robust results with significantly lower computational complexity and negligible errors by avoiding ill-conditioned mesh elements.