Disclosed herein are an apparatus and method for forming a 3D holographic image using non-periodically structured optical elements. The 3D holographic image apparatus includes a light source configured to radiate light, a spatial light modulator configured to modulate the light projected by the light source, and a non-periodic optical element configured to modulate incident light by refracting, diffracting or reflecting the direction of the incident light in a plurality of directions when the light modulated by the spatial light modulator is incident. A 3D holographic image may be formed based on the light modulated by the non-periodic optical element.