In low permeability reservoirs with conductive fractures, there is large capillary pressure contrast between the matrix and the fracture. It may cause very sharp changes in physical quantities near the matrix-fracture interface, which makes it difficult to calculate the matrix-fracture exchange flux accurately in the traditional embedded fracture model (EDFM). The strong capillary pressure contrast between the matrix and the fracture results in three flow patterns near the matrix-fracture interface and creates difficulty in calculation of the matrix-fracture exchange flux. In this article, a modified embedded discrete fracture model is proposed, where the analytical solutions for the three different patterns are employed to construct the numerical scheme for calculating the matrix-fracture exchange flux. The numerical tests show that the calculated results of the proposed model are in agreement with the reference model in which both the fracture cells and also the matrix cells near the fracture are subdivided sufficiently.