A high-pressure discharge lamp comprises a translucent ceramics airtight vessel (1) including an envelopment portion (1a) and a small-diameter cylindrical portion (1b) connected to the envelopment portion (1a) and having a sealing portion (SP). A current introducing conductor (2) is inserted in the inside of the small-diameter cylindrical portion (1b) including a sealing metal portion (2a) and a halogen-resistant portion (2b) connected each other. An electrode (3) is arranged at one end of the halogen-resistant portion (2b). The sealing portion (SP) is sealed by a fusion of melted poly-crystalline alumina ceramics of the small-diameter cylindrical portion (1b) at the sealing metal portion (2a) of the current introducing conductor (2), and the melted alumina ceramics includes aluminum grain growth control additives.
