Abstract: In this work, the non-linear flow behavior in anisotropic rough fractures is systematically studied.Synthetic rough fractures of different anisotropies that comply with rock surface geometric features as well aperture degrees are generated, and fluid flow in the rough fractures is simulated by numerically solving the Navier-Stokes equations.The influences of roughness, mean aperture and anisotropy on the non-linear seepage flow parameters are analyzed based on a numerically obtained relationship between pressure gradient and flow rate that are fitted by the Forchheimer equation.The research finds that the anisotropy ratio in apparent hydraulic conductivity increases with increasing relative roughness and aperture field anisotropy.A characterization model of non-Darcy coefficient based on the first-derivative root mean square roughness and equivalent hydraulic aperture is proposed, and the corresponding formula of critical Reynolds number is further derived.The proposed model can well describe the non-linear flow characteristics in anisotropic rough fractures and is in good agreement with previous experimental results.