There is provided an optical storage apparatus using a rewritable medium such a CD or MO cartridge which efficiently accurately measures eccentricity information that is necessary for an eccentricity correction and optimizes the eccentricity correction when a medium is loaded. Therefore, the optical storage apparatus comprises an eccentricity measuring unit (260) for measuring an eccentricity amplitude (Eamp) and an eccentricity phase (TΦ) for a start position of one rotation as eccentricity information on the basis of a detection of zero-cross points of a tracking error signal (E2) in a state in which the driving of the carriage (76) and lens (80) is stopped, an eccentricity memory (200) in which sine values corresponding to one rotation has been stored in correspondence to a rotating position of the medium (72, 82) and an eccentricity correcting unit for obtaining a medium eccentricity amount from the sine value read out from the memory (200) and eccentricity information measured by the measuring unit (260) and controlling a positioner (60) so as to set off the eccentricity amount.