Theoretical analysis shows that, to improve the resolution and the range of the field of view of the reconstructed image in digital lensless Fourier transform holography, an effective solution is to increase the area and the pixel number of the recorded digital hologram. A new approach based on the synthetic aperture technique and use of linear CCD scanning is presented to obtain digital holographic images with high resolution and a wide field of view. By using a synthetic aperture technique and linear CCD scanning, we obtained digital lensless Fourier transform holograms with a large area of $3.5\mathrm{cm}\times 3.5\mathrm{cm}$ ( $5000\times 5000$ pixels). The numerical reconstruction of a $4\mathrm{mm}$ object at a distance of $14\mathrm{cm}$ by use of a Rayleigh–Sommerfeld integral shows that a theoretically minimum resolvable distance of $2.57\mathrm{\mu m}$ can be achieved at a wavelength of $632.8\mathrm{nm}$ . The experimental results are consistent with the theoretical analysis.