Aperture synthesis is an effective means to improve the image resolution. For synthetic-aperture digital holography, an aperture synthesis method on sub-pixel displacement accuracy was proposed. The optical field was reconstructed by Fresnel diffraction formula based on fast Fourier transformation, and the displacement of hologram was transformed into piston phase and tilt phase by using the shift property of Fourier transformation, so that the digital holographic aperture synthesis with arbitrary displacement was realized. A digital off-axis holographic aperture synthesis experiment was carried out, and the experimental results verify the effectiveness of the proposed method. Furthermore, the method can effectively reduce the computational complexity under the premise of sacrificing a certain resolution, and has good real-time performance, and reduces the hardware configuration requirements of the processor.