A holographic display apparatus comprising: a light source configured to emit light; a spatial light modulator configured to sequentially display frames of hologram patterns for modulating the light to thereby sequentially reproduce frames of hologram images based on the frames of the hologram patterns wherein the hologram image for one frame comprises a first color image (HI R), a second color image (HI G), and a third color image (HI B), the first color image, the second color image and the third color image having different colors from each other; and a controller configured to provide hologram pattern data signals to the spatial light modulator, and configured to generate, for each frame, a hologram data signal component reproducing the hologram image, wherein the controller is configured to further generate diffraction pattern data signals for displaying periodic diffraction pattern components on the spatial light modulator, the periodic diffraction pattern components for adjusting locations of the hologram images reproduced on a hologram image plane, wherein the hologram image plane comprises each of one or more cross-sections constituting a three-dimensional image on a space, the periodic diffraction pattern component for a frame comprising a first periodic diffraction pattern for adjusting a location of the first color image, a second periodic diffraction pattern for adjusting a location of the second color image, and a third periodic diffraction pattern for adjusting a location of the third color image, the first periodic diffraction pattern, the second periodic diffraction pattern, and the third periodic diffraction pattern having different periods from each other, the controller being configured to set the periods of the first, second and third periodic diffraction patterns to be proportional to wavelengths of light of first, second and third colors, respectively, wherein, for a frame, the hologram data signal component and the periodic diffraction pattern component for a frame are formed together as a hologram pattern data signal and simultaneously displayed by the spatial light modulator; wherein the controller is further configured to move the periodic diffraction pattern components on the spatial light modulator along a predetermined direction for each of the frames. a light source configured to emit light; a spatial light modulator configured to sequentially display frames of hologram patterns for modulating the light to thereby sequentially reproduce frames of hologram images based on the frames of the hologram patterns wherein the hologram image for one frame comprises a first color image (HI R), a second color image (HI G), and a third color image (HI B), the first color image, the second color image and the third color image having different colors from each other; and a controller configured to provide hologram pattern data signals to the spatial light modulator, and configured to generate, for each frame, a hologram data signal component reproducing the hologram image, wherein the controller is configured to further generate diffraction pattern data signals for displaying periodic diffraction pattern components on the spatial light modulator, the periodic diffraction pattern components for adjusting locations of the hologram images reproduced on a hologram image plane, wherein the hologram image plane comprises each of one or more cross-sections constituting a three-dimensional image on a space, the periodic diffraction pattern component for a frame comprising a first periodic diffraction pattern for adjusting a location of the first color image, a second periodic diffraction pattern for adjusting a location of the second color image, and a third periodic diffraction pattern for adjusting a location of the third color image, the first periodic diffraction pattern, the second periodic diffraction pattern, and the third periodic diffraction pattern having different periods from each other, the controller being configured to set the periods of the first, second and third periodic diffraction patterns to be proportional to wavelengths of light of first, second and third colors, respectively, wherein, for a frame, the hologram data signal component and the periodic diffraction pattern component for a frame are formed together as a hologram pattern data signal and simultaneously displayed by the spatial light modulator; wherein the controller is further configured to move the periodic diffraction pattern components on the spatial light modulator along a predetermined direction for each of the frames.