DC arc plasma has become an important technology in the radioactive solid waste treatment. Based on the secondary development functions of Fluent with UDF and UDS, a two-dimensional axisymmetric magneto-hydrodynamic model was established in this paper, which correlates the simulation with physical properties of working gas, the source terms of governing equations and the current distribution on electrodes. By solving original equations (e.g. the Navier-Stokes equations) and Maxwell’s equations under reasonable boundary conditions., the temperature field, velocity field and current potential distribution were obtained The results show that, a) the electric potential drop near the cathode is significant and the current density distribution is concentrated; b) under laminar flow conditions, the temperature distribution in the arc column is uniform, the center temperature is the highest in the whole domain, and the temperature gradient in the plasma--cold-flow interaction region is large; c) there is a dense current distribution area near the anode, which can be used as the basis for predicting the arc root position. The research also lays a foundation for the coupling analysis of the electrode life and thermal efficiency.