We report a novel and non-iterative method for the generation of phase-only Fourier hologram for image projection. Briefly, target image is first added with a special quadratic phase and then padded with zeros. A complex Fourier hologram is generated via the simple fast Fourier transform. Subsequently, the error diffusion algorithm is applied to convert the complex hologram into a phase-only hologram. The numerical, as well as the optical reconstructed images with the proposed method are of higher visual quality and contain less speckle noise compared to the original random phase method, which add the random phase to the target image and then preserve the phase component of the complex hologram. The influences of quadratic phase and zero-padding on the image quality are also discussed in detail.