To efficiently form an excellent welding joint of stainless steel by a simple equipment.

The arc energy density is increased by converging the arc using the argon gas in which hydrogen gas of 1-7% is mixed as the shield gas. As for the dimensions of the V-shaped groove, the thickness t0 of the root surface is 0.1-1.5 mm, and the appropriate range of the V-shaped angle α is 65-80°, and a copper or ceramic backing having the groove of 0.5-1.5 mm in the depth (d) and 10-40 mm in width w1, is fixed to the inner side of the V-shaped groove, the molten metal is kept and cooled at the back side of the TIG arc, and the dimensional margin of the root gap of the V-shaped groove is expanded to 0-2.0 mm to achieve the excellent welding of austenitic stainless steel tubes to be joined with each other.