The paper presents a novel quasicrystal metasurface that can simultaneously reconstruct holographic images and exhibit diffraction patterns. By combining the quasi-periodic features of quasicrystals with the special rotational symmetry of metasurfaces, the authors design and fabricate a dielectric quasicrystal metasurface using nanostructures arranged in a quasi-periodic array. The metasurface combines the global arrangement of metasurfaces with the local responses (phase and amplitude) of meta-atoms to achieve dual functionality. The zero diffraction order in the far-field is suppressed based on the quasi-momentum matching rule. The proposed method has significant mathematical importance and explores new possibilities for multifunctional meta-devices, including holographic display, optical switching, and anti-counterfeiting. The authors demonstrate the dual functionality of the quasicrystal metasurface through experimental verification, showing that it can generate both holographic images and distinctive diffraction patterns. The design and fabrication process, as well as the experimental setup, are detailed, and the results are discussed in the context of their potential applications.The paper presents a novel quasicrystal metasurface that can simultaneously reconstruct holographic images and exhibit diffraction patterns. By combining the quasi-periodic features of quasicrystals with the special rotational symmetry of metasurfaces, the authors design and fabricate a dielectric quasicrystal metasurface using nanostructures arranged in a quasi-periodic array. The metasurface combines the global arrangement of metasurfaces with the local responses (phase and amplitude) of meta-atoms to achieve dual functionality. The zero diffraction order in the far-field is suppressed based on the quasi-momentum matching rule. The proposed method has significant mathematical importance and explores new possibilities for multifunctional meta-devices, including holographic display, optical switching, and anti-counterfeiting. The authors demonstrate the dual functionality of the quasicrystal metasurface through experimental verification, showing that it can generate both holographic images and distinctive diffraction patterns. The design and fabrication process, as well as the experimental setup, are detailed, and the results are discussed in the context of their potential applications.