Abstract: A glass preform for use in the fabrication of a single mode optical fiber having improved dispersion property is produced by a method comprising steps of forming a porous glass cladding body around a porous glass core body to form a porous glass preform while heating the core body to partially shrink the core body with adjusting a ratio of the shrunk part of the core body to that of the unshrunk core body at a value of 0.65 to 0.9 and then heating the porous glass preform to consolidate it to obtain a transparent glass preform. Preferably, the core body is partially heated and shrunk by a cladding forming burner.