Abstract: Quasi-crystal nano structures are often subjected to dynamic loads represented by elastic waves in engineering. In order to study their dynamic failure mechanism, Lamb waves in one-dimensional hexagonal quasi-crystal nano plates are investigated. Based on the Bak model, dynamic equations of Lamb waves are derived in the context of the modified couple stress theory. The Legendre orthogonal polynomial method is employed to solve the dynamic equations, and dispersion curves and displacement distributions are calculated. The size effect in phonon and phason fields, and the phonon-phason coupling effect on the wave characteristics are studied. The results show that the size effect increases the phase velocities of phonon modes and phason modes; the phonon-phason coupling effect significantly increases the amplitudes of phason displacements in the phonon modes and the amplitudes of phonon displacements in the phason modes. The results lay a theoretical foundation for the design and nondestructive testing of quasi-crystal nano structures.