In this study, lattice-gas cellular automata were used to solve the flow of incompressible Newtonian-fluid in porous media microchannels. We discuss fluid flow between two stationary parallel plates. By applying a constant pressure gradient, volumetric flux was determined as a function of time until a steady condition is achieved. For steady laminar flow, its velocity profile is parabolic. For flow in porous media between two stationary parallel plates, the results show that medium permeability depends on porosity and obstacle configurations. For a single obstacle, the permeability is a parabolic function with respect to positions of an obstacle in the direction perpendicular to the flow. The permeability is smallest when the obstacle is at the central line along the flow. A maximum permeability may be achieved when the obstacles attached to the channel wall. Other obstacle structures give lower permeability, even zero permeability for dead end microchannels.