In the fiber-drawing method, a first preform is lowered along a fiber-drawing axis through a fiber-drawing oven so as to be heated and drawn down into an optical fiber, and a second preform is lowered along the fiber-drawing axis through the fiber-drawing oven so as to be heated and drawn down in turn after the first preform has been withdrawn. While the first preform is being drawn down into a fiber, the second preform is heated in a preheating oven disposed adjacent to the fiber-drawing oven so as to raise the second preform to a temperature which is slightly below the fiber-drawing temperature, and the preheated second preform is transferred quickly onto the fiber-drawing axis after the first preform has been withdrawn therefrom. This method contributes to increasing the capacity for producing optical fibers.