A method for manufacturing a high-pressure discharge lamp includes a process step in which a sealing portion is formed out of a side tube portion of a glass pipe that is designed for use in a discharge lamp. In the step of forming the sealing portion, a compound glass tube, which is composed of an outer tube made of a first glass and an inner tube made of a second glass whose softening point is lower than that of the first glass, is inserted into the side tube portion, which is also formed of the first glass. The side tube portion is then heated so that the side tube portion is brought in tight contact with the compound glass tube. Thereafter, at least the sealing portion is heated at a temperature higher than the strain point temperature of the second glass portion.