There have been widespread concerns about solute transport problems in fractured media, e.g. the disposal of high-level radioactive waste in geological fractured rocks. Numerical simulation of particle tracking is gradually being employed to address these issues. Traditional predictions of radioactive waste transport using discrete fracture network (DFN) models often consider one particular realization of the fracture distribution based on fracture statistic features. This significantly underestimates the uncertainty of the risk of radioactive waste deposit evaluation. To adequately assess the uncertainty during the DFN modeling in a potential site for the disposal of high-level radioactive waste, this paper utilized the probabilistic distribution method (PDM). The method was applied to evaluate the risk of nuclear waste deposit in Beishan, China. Moreover, the impact of the number of realizations on the simulation results was analyzed. In particular, the differences between the modeling results of one realization and multiple realizations were demonstrated. Probabilistic distributions of 20 realizations at different times were also obtained. The results showed that the employed PDM can be used to describe the ranges of the contaminant particle transport. The high-possibility contaminated areas near the release point were more concentrated than the farther areas after 5E6 days, which was 25,400 m2.