Background <p>This paper investigates the dispersion characteristics of Lamb waves in porous functionally graded metamaterials (FGMM) plates of auxetic Graphene origami (GOri) under free boundary conditions.</p> Methods <p>The material properties are characterized using the Halpin-Tsai micromechanical model and Genetic Programming-assisted micromechanical models. Subsequently, based on the theory of elastic waves, the wave equations governing the propagation in the porous FGMM of auxetic GOri metamaterial plate are established. The Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) method is then employed to derive the dispersion equation for Lamb waves in the plate. The results are reduced to the case of an isotropic material and compared with existing literature results, validating the effectiveness and correctness of the proposed method.</p> Results <p>The dispersion equation is programmed and solved using mathematical software, yielding dispersion curves for various conditions, including different graphene mass fractions, porosity levels, folding degrees, and graphene distribution patterns.</p> Conclusions <p>The results demonstrate that these parameters significantly influence the dispersion effects. This study provides a theoretical and numerical foundation for understanding and applying the dispersion characteristics of elastic waves in porous FGMM of auxetic GOri plates.</p>