Regular Cartesian grid models provide satisfactory numeric results when a numerical scheme for reservoir flow simulation is applied. However, they cannot recreate complex geological features existing in realistic reservoir models such as faults and irregular reservoir boundaries. Corner point grids can represent these geological characteristics and can be adapted and represent any reservoir. In the subsurface reservoirs is usually typical to find fractures networks, and it is necessary to simulate the effect of them in reservoir models based on corner point grids. Although several works validate the precision of embedded Discrete Fracture Model (EDFM) for representing fractures in cartesian grids, very few studies have been presented to examine the accuracy of fracture modeling in geologically complex reservoir models. In this work, the novel discrete fracture model, the Projection-based Embedded Discrete Fracture Model (pEDFM), is implemented to represent fractures in reservoir models based on corner point grids. pEDFM provides additional features to the EDFM and is applied to explicitly and consistently define fractures. It implements independent grid sets for the fractures (described as lower-dimensional domains) and the rock matrix irrespective of the grid domains’ complex geometrical shapes. The suitability of the original pEDFM method has been expanded to a fully generic 3D geometry, and it lets on including fractures with any orientation on the corner point grid cells, an important development for the method’s viability in field-scale applications. Further to the geometrical flexibility of EDFM, matrix-matrix and fracture matrix connectivities are readapted to account for the projection of fracture plates on the interfaces. This allows for consistent modeling of fractures with generic conductivity values, from high conductive networks to impermeable flow barriers. A fully implicit scheme is used to get a discrete system with two main unknowns (i.e., pressure and phase saturation) on both matrix and fracture networks. Several 3D test cases of reservoirs models with complex corner point grids and fracture networks arbitrary designed in them are presented to demonstrate the devised method’s accuracy and applicability. The results show that the pEDFM implementation for two-phase flow is highly successful for modeling fractures with a broad range of conductivity on field-scale reservoir models.