The permeability in a fractured rock has obviously heterogeneous and anisotropic properties. To scientifically predict the groundwater flow characteristics of the fractured medium for a nuclear facility site, we put an emphasis on the uncertainty analysis of the hydraulic field in this paper. Methods: Based on the hydraulic test data, Pilot point calibration technique and null space Monte Carlo method were employed to establish the groundwater flow model. The corresponding uncertainties analysis was conducted to obtain a series of realizations that meet the hydrogeological conditions in support of the safety assessment. Results: The simulated hydraulic heads of different realizations were in a good agreement with the measured data. The numerical results could well reflect the actual hydrogeological conditions of the site. Besides, the hydraulic conductivity fields of different realizations exist some differences in the space domain. However, the overall change trends are similar. The variance of hydraulic conductivity filed around the boreholes is relatively low and is high in no borehole areas. Conclusions: NSMC method could well make up for the limitations of single and deterministic numerical model in characterizing the hydraulic conductivity filed in fractured medium, and effectively reduce the uncertainty and randomness of model parameters. It is positive to further improve the groundwater flow prediction ability. The simulations results could deepen the understanding of groundwater migration behavior in fractured rocks.