Layer-based hologram calculations generate holograms from RGB and depth images by repeating diffraction calculations using complex Fourier transforms (FTs). Holograms generated as such are suitable for near-eye display and can be easily reconstructed with good image quality, but they are computationally expensive because of multiple complex-valued operations, including complex FTs. In this study, we propose an acceleration method for layer-based hologram calculations by reducing time-consuming complex-valued operations using the real-valued FT and Hartley transform as real linear transformations. Real linear transformations transform real input data to real output data; thus, the proposed method generates amplitude holograms. Thus, we also propose a technique to convert holograms generated by real linear transformations into phase-only holograms using the half-zone plate process and digitalized single-sideband method while maintaining the calculation acceleration. The proposed method can speed up hologram calculations by a factor of around three while maintaining the same image quality as the conventional method.