Phase-only holograms (POHs) are often generated by the Gerchberg–Saxton (GS) algorithm. Nevertheless, low-quality reconstruction and iterative divergence plague the traditional GS method, reducing the quality of holographic display. Noise still affects adaptive weighted GS (AWGS) algorithms, despite their ability to ensure convergence through the addition of planned feedback. We propose an optimized AWGS algorithm, named optimized adaptive weighting constraints (OAWGS), for the generation of POHs for high-quality holographic display. The contrast and intensity of the signal domain are enhanced by adding a weighting factor to the AWGS feedback. By introducing non-signal regions and applying an optimized random phase as the initial phase, the OAWGS algorithm substantially improves the quality of holographic reconstruction. Compared with the AWGS algorithm, the proposed method can improve the peak signal-to-noise ratio by 5.45 dB and converge. It could reach convergence after 20 iterations. Both simulation and experiment results verify the effectiveness of the proposed method.