This paper examines the propagation characteristics of Love wave in a fiber-reinforced viscoelastic (FRV) layer imperfectly bonded over an underlying microstructural coupled stress half-space. The dispersion equations for Love wave propagation are derived using appropriate boundary conditions at both perfect and imperfect interfaces. The present mathematical model is validated by reducing the dispersion equation to the classical Love wave equation. A theoretical and graphical analysis of the effects of viscoelastic, reinforcement, microstructural, and imperfection parameters on the phase and damped velocity is presented. Numerical computations for the parameters involved were conducted with the aid of graphs. This study may have many applications in various fields, such as non-destructive testing techniques, biosensors, and seismology.