The paper investigates the dispersion of quasi-Lamb waves in a hydro-elastic system consisting of a plate of multilayer composite material and a compressible, inviscid fluid layer whose flow is confined by a rigid wall. The multilayer composite material is modeled as a transversely isotropic material whose axis of symmetry is aligned along the thickness of the plate. The motion of the plate is described by the exact equations and relations of elastodynamics for anisotropic bodies, but the fluid flow is described by the linearized Euler equations. The analytical solutions of these equations are found and according to these solutions the dispersion equations are obtained from the corresponding boundary, compatibility and impermeability conditions. The dispersion equation is solved numerically and the numerical results are obtained for the case where the plate material consists of two alternating layers. Based on these results, a parametric study of the influence of the density ratio of the plate and fluid materials and the ratio of the shear wave propagation velocity in the stiffer material layer of the plate to the sound velocity of the fluid on the dispersion curves with respect to the first four subsequent modes (denoted as A ₀, S ₀, A ₁ and S ₁ modes) of the quasi-Lamb waves is performed. The influence of the ratio of the shear moduli of the components of the multilayer material and the influence of the contact of the plate with the fluid are investigated.