The objective of the present work is to investigate the behavior of hydrogen in an atmospheric-pressure free-burning argon are when a small amount of hydrogen is added into the arc. A two-dimensional model calculation is carried out under the assumption that the ionization reaction of argon is in equilibrium and the reactions among hydrogen molecules, atoms, ions, and electrons are not necessarily in equilibrium. This calculation glues the following conclusion. The hydrogen mass fraction of 0.001 is too small to affect the flow and temperature fields markedly, and the concentration ratios among the hydrogen species are in equilibrium in the greater part of the arc region except for some parts with a steep temperature gradient. The hydrogen mass function, however, is not uniform in the arc and, especially in the high-temperature region near the cathode, over three times mass fraction of the hydrogen accumulates and flows downstream to cause a high flux of hydrogen atom toward the anode. This phenomena can be explained by the large difference between the diffusivity of hydrogen atom and that of hydrogen ion in argon ion.