A method of press-molding glass optical elements by press-molding glass, having a high melting point, at a temperature of 650.degree. C. and higher using a die for press-molding glass optical elements which includes a base material having a heat resistance and sufficient strength to withstand press-molding of optical glass elements, a cutting layer on the base material, and a surface protective layer on the cutting layer. The cutting layer is formed of an alloy film containing P and one metal selected from the group Ni, Co, and Fe, and one metal from the group Si, Ti, Cu, Zr, Nb, Mo, Ru, Rh, Pd, Hf, Ta, W, Re, Os, and Ir, or an alloy film containing Cu and 20 to 80 atom % of one metal selected from the group Ni, Co, Fe, Si, Ti, Zr, Nb, Mo, Ru, Rh, Pd, Hf, Ta, W, Re, Os, and Ir, or an alloy film containing Si and 20 to 80 atom % of one metal selected from the group Ni, Co, Fe, Cu, Ti, Zr, Nb, Mo, Ru, Rh, Pd, Hf, Ta, W, Re, Os, and Ir. The surface protective layer is formed of an alloy film of at least one metal selected from the group Pt, Pd, Ir, Rh, Os, Ru, Re, W, and Ta.