We provide a numerical procedure for the simulation of two-phase immiscible and incompressible flow in two- and three-dimensional discrete-fractured media. The concept of cross-flow equilibrium is used to reduce the fracture dimension from n to (n-1) in the calculation of flow in the fractures. This concept, which is often referred to as the discrete-fracture model, has a significant effect on the reduction of computational time. The spatial discretization is performed with the control-volume method. This method is locally conservative and allows the use of unstructured grids to represent complex geometries, such as discrete-fracture configurations. The relative permeability is upwinded with a criterion based on the evaluation of the flux direction at the boundaries of the control volumes, which is consistent with the physics of fluid flow. The system of partial differential equations is decoupled and solved using the implicit-pressure, explicit-saturation (IMPES) approach. The algorithm has been successfully tested in two- and three-dimensional numerical simulations of wetting phase fluid injection (such as water) in discrete-fractured media saturated by a nonwetting phase (such as nonaqueous phase liquid or oil) with mild to high nonlinearity in relative permeability and capillary pressure. To the best of our knowledge, results for simulations of two-phase immiscible and incompressible flow in three-dimensional discrete-fractured media, including capillary and gravity effects, are the first to appear in the literature.