An apparatus for generating a hologram that may generate a three-dimensional (3D) hologram pattern at a high speed may include a pattern setting unit to set points for which hologram patterns are to be generated with respect to a one-eighth area of an entire area for which a hologram pattern is to be generated, a calculation unit to calculate pattern values for a plurality of reference points selected with respect to the one-eighth area of the entire area, and to generate a pattern for the one-eighth area using recurrent interpolation, and a pattern duplicating unit to complete a pattern for the entire area by duplicating the generated pattern for the one-eighth area.