A production method and others according to the present embodiment are provided with a structure for effectively preventing occurrence of accidental spiking during drawing of a preform. In order to control the residual He-concentration in the center part of the preform, a transparent glass rod that has a predetermined outer diameter and is already sintered but is not doped with an alkali metal yet is annealed in in the atmosphere not containing He gas for an annealing time determined by referring to result data in which the relationship between the annealing time and the residual He-concentration is previously recorded for each outer diameter. In the result data, actually measured data of the residual He-concentration in a produced optical fiber preform and the annealing time are accumulated as annealing treatment results.