A speckleless illuminated modified-Gerchberg-Saxton-algorithm-type computer-generated hologram, which adopts a lower frequency of the iterative algorithm and calculation time, is proposed to code a hologram with two signals and position a multiplexing phase-only function, which can reconstruct the left and the right viewing holograms on the pupillary-distance position after the decryption and still maintain the content with high contrast and definition. The reconstructed image quality presents root mean square error of 0.03, with a diffraction efficiency of 87%, and signal-to-noise ratio of 8 dB after the analysis. Furthermore, two denoising techniques for the digital filter and optical suppression are combined, in which the speckle suppression with pseudorandom phase modulation and a rotating diffuser are utilized for successfully reducing the speckle contrast, which was reduced to below 4%. The goal was to reduce visual fatigue for the viewers.