A three-dimensional (3D) numerical analysis model of tungsten inert gas welding arc interacting with an anode material is presented based on the local thermodynamic equilibrium assumption and taking the behavior of metal vapor into account. The thermodynamic parameters and transport coefficients of plasma arc are dependent on the local temperature and metal vapor concentration. A second viscosity approximation is used to express the diffusion coefficient which describes the metal vapor diffuse in the argon plasma. The weld pool dynamic is described by taking into account the buoyancy, Lorentz force, surface tension, and plasma drag force. The temperature coefficient of the surface tension at the weld pool surface is considered in two ways: one is taken as a function of temperature with only oxygen being the active component, and the other is taken as a constant value. The distributions of temperature field and velocity field of arc plasma and weld pool, metal vapor concentration and current density in the arc plasma are investigated by solving the Maxwell equations, continuity equation, momentum conservation equation, energy conservation equation and the components of the transport equation. The influence of metal vapor on arc plasma behavior and that of arc plasma on the weld pool are studied and compared with the non-metal vapor results. It is shown that the distribution of Fe vapor concentrates around the weld pool surface. Metal vapor has obvious shrinkage effect on arc plasma, and weak influences on velocity and potential of the arc plasma. In addition, the metal vapor has a weak effect on the distributions of velocity and shear force on the weld pool surface and no obvious influence on the molten pool shape. We test two different methods to illustrate this point in the case with or without metal vapor. The method used for a variable temperature coefficient of surface tension allows the prediction of a depth-to-width ratio and weld pool shape in agreement with experimental result when taking the behavior of metal vapor into account. The results in this paper, obtained by simulation are in good agreement with experimental results and also with the simulation results by some other authors.