The problems concerned with the dispersion and attenuation of surface wave propagations due to imperfect elasticity are of great interest to seismologists. The present work reports the dispersion and attenuation characteristics of Love-type wave propagation in a fiber-reinforced layer laid on an inhomogeneous viscoelastic half-space. The inhomogeneity in the viscoelastic medium arises due to the hyperbolic trigonometric variation in depth. A complex frequency equation for the Love-type wave has been procured using the suitable boundary conditions. Thus, the dispersion and damping equations have been calculated to analyze the dispersion and attenuation peculiarities of the wave. Results for the uniform homogeneous isotropic media have been compared with existing solutions. Numerical computation and graphical sketches have been set forth for the relevant parametric variations. © 2019, Allerton Press, Inc.