A digital rainbow hologram (DRH) is a potential next-generation three-dimensional display media for the development of modern and smart electronics devices. It is one of the methods that can support the characteristic whereby a realistic display media occupies the space that the real object would have occupied. Since a rainbow hologram records a large amount of spatial or temporal frequency component from the object that represents the rainbow spectrum, a large amount of information needs to be decoded digitally. In this paper, to reconstruct a DRH, we propose a novel method based on the modulation of red, green, and blue spectral components of light by wavelet transform (WT) in the recording and reconstruction processes, which we digitally simulated in a computer using an algorithm. In the simulations, continuous WT (CWT) was based on Haar, Daubechies, Meyer, and Coiflet wavelets with a level set to be two. Based on the results of simulations using CWT, the optimum distance between object and hologram was 30 cm, and the maximum compression was 88.55%, which was achieved with Meyer wavelet. Moreover, optimal de-noising and optimal localization of spatial frequency component based on red, green, and blue spectral components were also achieved using the proposed method.