An apparatus for compensating for a defect of a storage medium of an optical driving includes a memory to store sample values of a servo driving signal during at least one track sampled by a first signal and cycle information about the first signal; a servo driving signal estimator to estimate a servo driving signal during at least one next track using the sample values, the cycle information about the first signal, and cycle information based on a second signal; and a transmitter to transmit the servo driving signal estimated by the servo driving signal estimator to a servo driver of the optical driving device during a defect section of the storage medium; wherein the first signal is synchronized with a radial direction of the storage medium; and the second signal has a frequency higher than the first signal.