At present, spatial light modulators are incapable of modulating both the amplitude and phase of the wavefront simultaneously. Therefore, when a spatial light modulator is used for holographic display, it is necessary to encode the complex amplitude of the object wave into amplitude-only or phase-only computer-generated-hologram. The phase-only holographic display has attracted much attention of researchers due to its characteristics of high diffraction efficiency and no conjugate image. However, current optimization algorithms for generating phase-only hologram have the problems of iterative divergence, slow convergence speed, and poor reconstruction quality, which is difficult to satisfy the requirements for high-quality holographic display. In this work, we propose an accurate adaptive mixed constraint Gerchberg-Saxton algorithm by constraining the frequency bandwidth in the hologram plane and adaptively constraining the amplitude of the reconstructed image in the image plane based on the angular spectrum propagation theory. Firstly, we use the angular spectrum propagation model without paraxial approximation to simulate the forward and backward propagation of the light wave for ensuring the accuracy of the wavefront propagation. Secondly, dividing the image plane into signal area and noise area according to the spatial distribution of target image, and different adaptive feedback strategies are set up for the two regions based on the optimized effect of the phase-only hologram. The adaptive feedback strategy is established, which can accelerate the convergence speed of the proposed algorithm and enhance the hologram of freedom of the optimization. Finally, the frequency bandwidth constraint strategy is introduced in the hologram plane to optimize the edge pixels and compensate for the frequency information loss of the phase-only computer-generated hologram, which improves the reconstruction quality of the hologram. After 100 iterations, the average correlation coefficient of the holographic reconstructed image of the proposed algorithm is about 0.9857, and the average peak signal-to-noise ratio is about 31.02 dB. The correlation coefficient and the peak signal-to-noise ratio of the reconstructed images of the proposed algorithm are better than those of the Gerchberg-Saxton algorithm with only frequency bandwidth constraint strategy, and the proposed algorithm has clearer texture and better display effect. The results of numerical simulations and optical experiments show the feasibility and effectiveness of the proposed method. The proposed adaptive mixed constraint Gerchberg-Saxton algorithm is a promising technology for high-quality holographic display.