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The main problem faced by traditional three-dimensional (3D) holographic displays is the time-consuming and poor flexibility of the hologram generation process. To address this issue, this paper proposes a non-iterative 3D computer-generated hologram (SFS-ORAP-PC-3D) method based on single full-support optimized random phase and phase compensation. Combining the full-support optimized random phase (FS-ORAP) method and the 3D layer-based idea to efficiently and non-iteratively generate the phase-only hologram of a 3D object with arbitrary positions and sizes using single FS-ORAP, thus overcoming the limitations of the original ORAP method in target position and size. Meanwhile, using a Fresnel lens for phase compensation allows for free selection of reconstruction planes. Numerical and optical experiments validate the feasibility of our proposed method.