The invention relates to a stainless steel tube and its making technology, and concretely relates to a precise stainless steel tube for a nuclear power unit, and its making technology. The precise stainless steel tube comprises the following components, by mass, 0.04-0.05% of C, 0.15-0.3% of Si, 0.8-1% of Mn, 13-15% of Ni, 15-17% of Cr, 0.2-0.4% of Nb, 2.5-3.5% of Cu, 0.15-0.2% of N, 0.15-0.25% of Mo, 0.2-0.3% of Al, 6-8% of lanthanide rare earth, and the balance Fe. The limitation of the components and technological parameters, the addition of proper amounts of lanthanide rare earth elements, and the pure hydrogen protection gas bright-heat treatment operation make the stainless steel tube have a good corrosion resistance, and simultaneously the internal surface roughness, the external surface roughness, the yield strength, the tensile strength and the like of the precise stainless steel tube for a nuclear power unit are high.