Single rough-walled fracture and surrounding rock matrix are the basic units that compose the discrete fracture network, so it is of great significance to study the fluid flow behaviors in it. A series of numerical simulations by directly solving the Navier- Stokes equation were carried out to study the influence of surface roughness, matching degree and matrix permeability on non- Darcian flow in three-dimensional single rough-walled fracture. The results review that the Forchheimer equation can accurately characterize the nonlinear relationship between the flow rate and pressure gradient in single fracture in fracture-matrix model. The increase of surface roughness and the degree of mismatch aggravates the inhomogeneity of aperture distribution, increases the flow resistance of the fracture and facilitates the non-Darcian flow. By contrast, the permeable matrix enhances the flow through the fracture, and the flow rate through the rough single fracture can be increased by up to 14%, which inhibits the non-Darcian flow. The influence level of matrix permeability on the growth of fracture flow capacity is positively correlated with surface roughness and degree of mismatch.