A two-dimensional axisymmetric steady-state arc model and a three-dimensional current density distribution model are established in this study, and the effects of electrode embedded with magnesia-carbon material on electrode current density distribution and DC arc characteristics are studied. The results show that when the electrode embedded with magnesia-carbon material is used, the magnesia-carbon material in the electrode is not conductive, and the maximum current density (excluding cathode spots) increases with the increase of the radius of the magnesia-carbon material. Moreover, with the increase of the radius of magnesia-carbon materials, the maximum temperature and maximum axial velocity in the center of the arc, the maximum value of shear force, heat flux and pressure of arc on anode center are reduced, the position of the maximum temperature and the position of the maximum axial velocity migrate from near the cathode to the anode. The other temperature ranges first increase and then decrease in the radial direction, the shear force, heat flux, and pressure of arc on area within a certain distance from the center increases. Therefore, the appropriate radius of magnesia-carbon material can improve the heat transfer conditions and dynamic conditions of the arc on the area near the molten pool center.