Fracture has significant effect on the production of hydrogen–carbon compound reservoirs. Underground fluid always flows through different spaces which involves different flow patterns. In this study, the embedded discrete fracture method (EDFM) to couple the flow in matrix and fracture is introduced. The Darcy flow is considered in fracture while the Pre-Darcy flow is employed in matrix. The model of two phase flow problem is established. The governing equations are coupled through multiple spatial scales. The structured mesh is applied to discrete the whole matrix domain. The fracture grids are embedded to the matrix meshes. The verification shows good accuracy of the fully implicit method for solving the model. Based on the numerical simulation, the results of 1D, 2D flow problems considering Pre-Darcy flow are presented. The characteristic of pressure and saturation is analyzed. Some numerical experiment examples are conducted to demonstrate the capability of the method including multiple wells system, complex fracture problem, and hydraulic fractured horizontal well system. Furthermore, we extend the model to 3D transport problem. The newly developed numerical simulation method improves the limitations of EDFM in Pre-Darcy flow. The newly developed simulation method can be taken as an effective tool for hydrocarbon production analysis when Pre-Darcy flow happens in fractured porous media.