In this paper, a method of speckle noise suppression for holographic zoom display based on layered-pixel-scanning (LPS) algorithm is proposed. Different from the traditional algorithm, the proposed method suppresses the speckle noise based on a new algorithm design and light source optimization. The LPS algorithm is designed to calculate the phase-only hologram of the 3D object. By extracting the initial complex hologram of the 3D object and scanning the hologram by pixel, the errors of the complex amplitude can be reduced as much as possible. Then a hologram subsampling method based on the LPS algorithm generated is proposed, so the scaling of the reproduced image can be achieved easily. At the same time, the pattern with different random phase is generated and loaded on the spatial light modulator so that the reconstructed light can be optimized. When the optimized light irradiates on the phase hologram of the object, the reconstructed image with suppressed speckle noise can be displayed. The experimental results show that the proposed method has an excellent reproduction effect. Moreover, the feasibility and unique advantages of the proposed method in the holographic augmented-reality display, zoom display and multiplane display have been proved. We believe that this method can promote the application of the holographic display.