The propagation characteristics of laser-generated Lamb wave in the three-dimensional thin viscoelastic plate are studied. Based on the theory of the stress-strain relation, the three-dimensional equation of dynamic equilibrium in the frequency domain is derived. Taking account of the viscoelastic property of the material, the three-dimensional model of laser-generated Lamb wave in the frequency domain is established by the finite element method. The process of laser-generated Lamb wave and its propagation are simulated in the three-dimensional thin viscoelastic plate. The numerical results coincide well with the characteristics of the group velocity curve, dispersion curve and attenuation curve which calculated by the analytical method. The results show that the velocities of the s0 and a0 modes increase gradually and the dispersive nature of the a0 mode decreases with the direction normal to the fiber direction gradually turning to the direction along the fiber direction in the unidirectional fiber-reinforced thin viscoelastic plate. In addition, the increase of source-receiver distance along the same direction causes a marked increase in the attenuation of Lamb waves and the attenuation of the higher-frequency signal is stronger than the lower-frequency one.