Provided is a holographic display apparatus including a motor configured to synchronize with a hologram transmitted based on user's point of view and to rotate; a spatial light modulator configured to load hologram data generated based on the user's point of view in a fixed position state and to perform a light modulation; a mirror configured to provide the hologram which is light-modulated by the spatial light modulator according to the user's point of view during the rotation by rotation operation of the motor; and a hologram correction unit configured to compensate a rotation error between the fixed spatial light modulator and the rotating mirror and to provide a corrected hologram data to the spatial light modulator.