This article deals with the study of propagation of shears waves in a composite structure consisting of a piezoelectric layer superimposed on a layer of fiber-reinforced material. A mathematical model is framed and the dispersion relation of shear wave is derived analytically. By suitable substitutions the dispersion relation obtained is reduced to the well-known classical Love wave equation. The effects of various parameters such as wave number, thickness ratio and the direction of fiber-reinforced parameters on the shears wave velocity has been investigated and depicted graphically.