The presented analytical study deals with the propagation of shear waves (S waves) in the layered structure containing an orthotropic material layer bonded with an heterogeneous viscoelastic half-space. Separate governing differential equations are applied while obtaining the analytical solution of transverse displacement in the respective media. The dispersion relation (complex form separated into real and imaginary parts) is finally derived in the closed form for the considered system employing suitable boundary conditions and the derived displacements. The obtained results are also shown to match with the classical Love waves equation (for isotropic media case). The phase- and damping velocity terms are plotted against the wavenumber (all quantities in dimensionless form) for the different values of material parameters. The effect of heterogeneity parameter, viscoelastic parameter, and the layer thickness on the wave propagation is graphically presented that can be used while exploring the nature of S wave propagation through similar composite structures. © 2022