An optical fiber preform 2 having a viscosity ratio Reta=eta0/etat of 2.5 or less between the core average viscosity eta0 and the total average viscosity etat is prepared, and is drawn by a drawing furnace 11 so as to yield an optical fiber 3, which is then heated to a temperature within a predetermined range so as to be annealed by a heating furnace 21 disposed downstream the drawing furnace 11. Here, upon annealing in the heating furnace 21, the fictive temperature Tf within the optical fiber lowers, thereby reducing the Rayleigh scattering loss. At the same time, the viscosity ratio condition of Reta<=2.5 restrains the stress from being concentrated into the core, thereby lowering the occurrence of structural asymmetry loss and the like. Hence, anoptical fiber which can reduce the transmission loss caused by the Rayleigh scattering loss and the like as a whole, and a method of making the same can be obtained.