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Acoustic holography is an essential tool for controlling sound waves, generating highly complex and customizable sound fields, and enabling the visualization of sound fields. Based on acoustic sieve metasurfaces (ASMs), this paper proposes a theoretical design approach for zero-thickness broadband holograms. The ASM is a zero-thickness rigid screen with a large number of small holes that allow sound waves to pass through and produce the desired real image in the target plane. The hole arrangement rules are determined using a genetic algorithm and the Rayleigh–Sommerfeld theory. Because the wave from a hole has no extra phase or amplitude modulation, the intractable modulation dispersion can be physically avoided, allowing the proposed ASM-based hologram to potentially function in any frequency band as long as the condition of paraxial approximation is satisfied. Using a numerical simulation based on the combination of the finite element method (FEM) and the boundary element method (BEM), this research achieves broadband holographic imaging with a good effect. The proposed theoretical zero-thickness broadband hologram may provide new possibilities for acoustic holography applications.