In this work, we present a numerical treatment for the model of two-phase flow in porous media including specific interfacial area. For numerical discretization we use the cell-centered finite difference (CCFD) method based on the shifting-matrices method which can reduce the time-consuming operations. A new iterative implicit algorithm has been developed to solve the problem under consideration. All advection and advection-like terms that appear in saturation equation and interfacial area equation are treated using upwind schemes. Selected simulation results such as pc–Sw–awn surface, capillary pressure, saturation and specific interfacial area with various values of model parameters have been introduced. The simulation results show a good agreement with those in the literature using either pore network modeling or Darcy scale modeling.