The anode region of a dc glow discharge at low pressure and current is studied by a new self-consistent, spatially one-dimensional hybrid method. The method consists of the coupled solution of the steady-state fluid equations of electrons, ions, and excited atoms and the Poisson equation using the electron transport properties as well as the excitation and ionization frequencies from a strict solution of the non-uniform kinetic equation of the electrons. Results such as the electric potential, the electron velocity distribution function, and the densities of the charge carriers and excited atoms are reported for the anode region of neon glow discharges. Physical properties of the plasma in the anode region known from experiments have been confirmed by the model such as the occurrence of the anode fall, a formation of plateau-like areas of the potential profile in front of the anode, the anode dark space, and the anode glow.