With the method of gas-driven permeation, a series of permeation experiments was carried out using Hastelloy N alloy membrane in an elevated temperature range of 400°C to 800°C with different hydrogen isotopes. A complete set of permeability, diffusivity, and Sieverts’ constant for hydrogen and deuterium in Hastelloy N alloy was successfully obtained. The isotope effect in the diffusion process was analyzed and compared with references. The ratios of diffusive transport parameters for hydrogen and deuterium were a permeability ratio of ФHD = 1.32exp(0.34kJ/RT), a diffusivity ratio of DH/DD = 1.15exp(−0.41kJ/RT), and a Sieverts’ constant ratio of KS,H/KS,D = 1.16exp(0.21kJ/RT). The result that the permeation flux of deuterium was decreased after introducing hydrogen could be used to suppress the permeation of tritium in future tritium control of the Fluoride-salt-cooled High-temperature Reactor (FHR). Compared with NiO, the Cr2O3 formed in the surface oxidation layer of Hastelloy N alloy showed better hydrogen permeation barrier performance after baking above 700°C in air.