Based on the theory of magnetohydrodynamics， the mathematical models of different current densities for TIG （tungsten inert gas） arc with external longitudinal magnetic field were established in the rotating cylindrical coordinate system. The flow field and electromagnetic field were coupled by fluent user-defined function， and the results show that the temperature field of TIG arc under longitudinal magnetic field presents the shape of hollow bell， and the distribution is bimodal， but a zone of low temperature occurs near the anode. With the increasing of current density， zone of "low temperature cavity" becomes larger near the anode surface. In addition， effect of longitudinal magnetic field on the pressure of anode surface is also distributed in double peak， and the peak pressure decreases by about 70% compared with that without magnetic field. And the dropping become sharper with the increasing of current density.