Abstract: Based on the linear three-dimensional elasticity theory and "Incremental Deformation Mechanics" theory, the wave equations of acoustoelastic Lamb waves propagating along the non-principal symmetry axes direction of fiber reinforced composite lamina were derived by using Legendre orthogonal polynomial expansion method when the initial stresses were applied horizontally and vertically. The wave equations were solved numerically. In order to verify the accuracy of the method, the dispersion curves of phase velocity for isotropic material obtained by the author’s method were compared with that from "Disperse^®". The stress distributions of wave structure without initial stress were computed and compared with the initial condition of stress free boundary by taking a fiber reinforced composite lamina as an example. The effects of horizontal and vertical initial stresses on the dispersion curves of Lamb waves were studied. Because the Lamb wave A₀ mode was more sensitive to the acoustoelastic effect, the influence of initial stresses on the displacement distributions of wave structure was investigated.