The invention discloses a welding method for an annular header, which is capable of greatly reducing stress concentration. According to the welding method, all oblique nozzles are arranged and fixed at first, and then welding is started; and welding is divided into three steps: 1, fixed-position welding, wherein tungsten inert gas welding is adopted in the fixed-position welding, two sections of connected arc welding areas are arranged at the butt-joint part of each adjacent oblique nozzles and have different arc lengths, the relatively long arc welding area is a first arc welding area, and the relatively short arc welding area is a second arc welding area; 2, backing welding, wherein tungsten inert gas welding is adopted in the backing welding, the annular header is provided with six welding areas in total, which are a welding area A, a welding area B, a welding area C, a welding area D, a welding area E and a welding area F, and the six welding areas are clockwise arranged; and 3, welding seam-filling welding, wherein welding is carried out by virtue of a manual electric arc welding method in the welding seam-filling welding, odd layers and even layers are reversely welded, and so on, until the filling welding is completed. The welding method disclosed by the invention has the advantage of basically no stress concentration.