The paper presents results of numerical investigation of a large-volume plasma source based on a DC discharge with gridded anode. Geometry and configuration of the electrodes were chosen so as to ensure the formation of a cathode sheath, which would accelerate electrons up to high energies and inject them into the post-Anode space and create plasma. Simulations were carried out using a hybrid model, and distributions of the main discharge parameters were obtained in a wide range of currents. At low currents, cathode sheath occupies whole interelectrode gap while plasma is formed in the post-Anode space. It is shown that ions moving through the anode grid into the interelectrode gap cause reduction of discharge voltage when compared to the case of classical obstructed discharge with virtually closed anode grid. At higher currents, however, plasma is formed within the interlectrode gap as well, and ions moving from plasma in the post-Anode space become trapped by reversed electric field. This essentially nullifies influence of the post-Anode plasma on discharge properties.