The diffuse and constricted arc attachment modes to the anode of an argon wall-stabilized transferred arc are investigated using a 2D chemical non-equilibrium model. Detailed argon chemical kinetic processes and self-consistent effective binary diffusion coefficient approximation treatment of diffusion are coupled with a single-fluid, two-temperature model to investigate the plasma characteristics of the near-anode region. The diffuse and constricted arc attachment modes to the anode are obtained self-consistently by changing the gas flow rates. The results show that the high current density and associated self-induced magnetic field of the constricted arc attachment give rise to a large Lorentz force near the anode, resulting in an anode jet. The convection process dominated by the cathode jet is conducive to the radial transport of electrons in the diffuse arc attachment mode, while in the constricted arc attachment mode the direction of electron transport due to the convection caused by the anode jet is opposite to that in a diffuse arc attachment. The effect of diffusion on electron transport is relatively small in the arc central region, while it becomes important in the arc fringe. The recombination processes, especially the dissociative recombination reactions, restrict the electron radial diffusion in the arc fringe. The diffusion current density is the main component of current density in front of the anode due to the steep gradient of electron pressure. It is found that when the diffusion current is not considered, the electric field and Joule heating in front of anode promote a more constricted arc attachment.