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This paper proposes a numerical model for the fluid flow in fractured porous media with the extended finite element method. The governing equations account for the fluid flow in the porous medium and the discrete natural fractures, as well as the fluid exchange between the fracture and the porous medium surrounding the fracture. The pore fluid pressure is continuous, while its derivatives are discontinuous on both sides of these high conductivity fractures. The pressure field is enriched by the absolute signed distance and appropriate asymptotic functions to capture the discontinuities in derivatives. The most important advantage of this method is that the domain can be partitioned as nonmatching grid without considering the presence of fractures. Arbitrarily multiple, kinking, branching, and intersecting fractures can be treated with the new approach. In particular, for propagating fractures, such as hydraulic fracturing or network volume fracturing in fissured reservoirs, this method can process the complex fluid leak-off behavior without remeshing. Numerical examples are presented to demonstrate the capability of the proposed method in saturated fractured porous media.