A stretching method and apparatus of an optical fiber base material including gripping both ends in a longitudinal direction of an optical fiber base material by a pair of gripping devices, and, while pulling the optical fiber base material by moving one or both of the pair of the gripping devices in a first direction parallel to the longitudinal direction, moving a heating device relative to the optical fiber base material in a second direction opposite to the first direction, wherein stretch of the optical fiber base material is performed while changing the relative moving speed Vb(x) in accordance with expression (1): Vb·[Dmax/D(x)]2≦Vb(x)≦Vb·[Dmax/D(x)]3  (1) where Vb represents a reference speed, Dmax represents a maximum outer diameter of the optical fiber base material, D(x) represents an outer diameter at a heated position x of the optical fiber base material, and Vb(x) represents a relative moving speed of the heating device relative to the optical fiber base material at the heated position x.