For tight reservoirs/formations, flow in fracture and matrix obey different flow patterns. Pre-Darcy flow always exists in low permeability subsurface porous media while Darcy flow can be applied in fracture. It is an outstanding challenge to understand the flow behavior coupling different flow mechanisms. As numerical simulation can predict field-scale performance so the development of efficient simulation method becomes a key issue to evaluate the flow behavior. In this paper, we develop an improved discrete fracture model based on the widely used embedded discrete facture model (EDFM) to simulate the transport both in homogenous and heterogeneous porous media in the presence of Pre-Darcy flow. The conservation equations are derived for fracture and matrix firstly and then discretized by fully implicit method. The transmissibility of different connection types is defined and the detailed calculation workflow is presented as well. The proposed model is verified through the comparison with the model using local grid refined (LGR) method. It is discovered that our simulation method exhibits good accuracy when analyzing the effect of Pre-Darcy flow. Some examples are shown including 1D scalar transport, 2D heterogeneous, 3D flow, complex fracture system and multiple well system problems with fully-coupled flow in fracture and matrix. The pressure distribution and well flux are demonstrated to analyze the Pre-Darcy flow characteristics. Results indicate that the new model works robustly for different flow problems which provide further insight into the Pre-Darcy flow in low permeability media.