A method for manufacturing a single mode optical fiber with a reduced PMD (Polarization Mode Dispersion), by drawing an optical fiber preform composed of a core and a clad surrounding the core, includes (a) heating the optical fiber preform to a high temperature using a furnace, and drawing an optical fiber from an outlet of the furnace at a linear velocity (V.sub.f) of 500 mpm or above by means of neck-down drawing; and (b) impressing a spin on the optical fiber by means of a spin impressing device provided on a drawing path of the optical fiber, wherein a maximum spatial frequency of spin (y) impressed on the optical fiber satisfies the following equations.function..times..ltoreq..ltoreq..times. ##EQU00001## and t=(0.21.times.CladOval)+(0.04.times.CoreOval)+(0.17.times.ECC), where y is a maximum spatial frequency of spin [turns/m], V.sub.f is a drawing velocity [mpm], CladOval is a clad ovality [%], CoreOval is a core ovality [%], and ECC is an eccentricity [.mu.m].