In this work, the Magneto-Hydrodynamic (MHD) model basedon the magnetic vector potential description is used to simulate a DC argonfree-burning plasma arc. The temperature and velocity fields of the arc areobtained by solving the electromagnetic equations and hydrodynamic equationswith the coupled iterative computation. The simulation results that clearlyshow the phenomenon of high temperature cathode jet of plasma-arc arecompared with the other research results. The effect of the cathode sheathto the simulation results is analyzed specially in this paper. For the argonfree-burning arc, the characteristics of plasma arc flow and heat transferunder different arc current conditons have been obtained, which providessome useful knowledge for industrial applications of arc plasma.