A fluid model of direct-current (DC) discharge in argon atmosphere between the gaps of rod-plane electrode configuration was established, and the discharge models of two geometrically similar gaps were solved using the finite-element method, respectively. The dimension ratio of the gaps was set as 10:1, and the gas pressure was ～133.3 Pa for the prototype and ～133 Pa for the scale-down gap; to the gaps the same DC voltages were applied. Voltage-current characteristics, as well as the physical discharge parameters (such as electric potential, electric field, electron density, ion density, and electron temperature) were obtained. Relations between parameters of the two gaps were investigated according to the theoretical relations derived by similarity law. Simulation results show that the discharge type in the two similar gaps is verified as a normal glow discharge; the parameter relations are in good agreement with the similarity law, and the working points of discharges are identical in similar gaps with the same applied DC voltage. This study could offer theoretical instruction in extrapolating the discharge properties for similar gaps.