The phenomenon of natural convection flow in a vertical cylindrical enclosure filled with unbound porous medium saturated by a Newtonian fluid has been investigated. The finite-difference method is performed to investigate the influence of uniform and non-uniform porosity along the z axis. The results of the numerical simulation obtained, presented in terms of streamlines, isotherms, local Nusselt number and average Nusselt number shows the dependence of the fluid flow pattern and the rate of heat transfer near to the heat wall on the variation of porosity is significant. The variation of the porosity along the z axis enhances the strength of fluid circulation. It is observed that the change from conduction dominant to convection dominant is obtained for low values of Rayleigh number in the case of variable porosity. Also, it is observed that an increase of Rayleigh number leads to an increase of the average Nusselt number while depending on the fluid flow pattern