A mercury-free high-pressure discharge lamp includes a light-transmissive airtight envelope enclosing therein a discharge space, and a pair of electrodes sealed inside the light-transmissive airtight envelope and facing the discharge space, and the primary halide includes at least thulium bromide having an innumerable emission spectrum primarily around the peak of a luminosity curve and alkali metal halide, and the accessory halide contains one or more metal halides mostly selected from a group of Magnesium (Mg), Iron (Fe), Cobalt (Co), Chromium (Cr), Zinc (Zn), Nickel (Ni), Manganese (Mn), Aluminum (Al), Antimony (Sb), Bismuth (Bi), Beryllium (Be), Rhenium (Re), Gallium (Ga), Titanium (Ti), Zirconium (Zr), and Hafnium (Hf) which primarily contribute to fix lamp voltage.