The present invention is to obtain a glass bulb of reduced weight, and high safeness and reliability by ion exchanging which assures a compressive stress layer having an effective thickness even to a large tensile vacuum stress. For this purpose, a region in an outer surface of a body portion 4 of the glass funnel, the region having a small mechanical strength and producing the maximum tensile vacuum stress thereby causing breakage easily, is partly strengthened by ion exchanging method according to an electric field assisting method and an ion exchanging method using paste in combination, whereby a portion 9 strengthened by ion exchanging method is provided in that region wherein the concentration of doped ions in a strengthened compressive stress layer is distributed according to a substantially step function in a direction from the surface of the glass toward the inside of it.