We provided an approach to estimate hydraulic diffusivity of a single fault by solving the linear diffusion equation in a partly open rough fracture under drained conditions when applying small pressure drop fluctuations (10^-5 Pa) along the fault. In contrast to the traditional calculation for the fracture hydraulic diffusivity using parameters such as hydraulic aperture, fluid compressibility, fluid viscosity, we here directly used time-dependent pressure profile p(x, y, t) to match the analytical solution for an equivalent parallel plate model, which contains hydraulic diffusivity as unknown. The method considered transient pressure diffusion process, which might give a more accurate value for hydraulic diffusivity compared to traditionally calculated one. Our results under large closure (hydraulic diffusivities are of orders 10^2 m2/s – 10^4 m^2/s) are consistent with the values derived from analysis of some earthquake sequences (Noir et al., 1997; Antonioli et al., 2005; Malagnini et al., 2012; Dempsey and Riffault, 2019; Schmittbuhl et al, 2021). Those earthquakes were assumed to be triggered by the diffusion of pore pressure perturbation in a fractured medium, and the seismicity migration was then evidenced to be compatible with pore pressure relaxation. The hydraulic diffusivity estimated by Noir et al. (1997) for the 1989 Dobi earthquake sequence of Central Afar ranges between 10^3 – 10^4 m^2/s, which corresponds to the characteristic width (i.e., effective aperture) 1 mm - 3 cm. The consistency with our results indicates that our model might be used to predict potential earthquake migration, in particular, when a single fault path dominates the fluid flow. Compared to diffusivities estimated from direct hydraulic tests, the values obtained from our simulations are somehow large. The discrepancy could be attributed to several aspects: the diffusivity from direct hydraulic test is commonly affected by fracture networks instead of a single fault, and combines matrix diffusivity and fracture diffusivity (Ortiz R et al., 2013; Sayler et al., 2018), which lower the value. In addition, it also depends on temperature, mineral sealing, fault movement and tested methods, e.g., lower hydraulic diffusivities were observed in constant rate tests than periodic tests (Guiltinan and Becker, 2015). In cases that fluid flow was dominated by a constrained planar fracture., e.g., Sayler et al. (2018), it was evidenced that flow between an interval with large diffusivities (up to 10^3 m^2/s). We also compare our results to the hydraulic diffusivity assessment for the recent Strasbourg earthquake sequence: 25 m^2/s (Schmittbuhl et al, 2021). Our approach can be extended to estimate hydraulic diffusivity for fracture networks when considering roughness (varied aperture distribution) for each fracture (Haagenson and Rajaram, 2021).