Love waves in a pre-stressed fiber-reinforced medium lying above a monoclinic half-space have been investigated. Upper surface of fiber reinforced layer remains stress free and interface of half space and layer satisfies continuity conditions .The dispersion equation for Love waves propagation has been derived. Effect of anisotropy parameter of half space and initial stresses of reinforced layer on Love waves propagation have been observed from dispersion curves. Some particular cases have also been developed by using the dispersion equation. Further, the range of the existence of Love waves is calculated. The cut-off periods for three nodes of Love waves with variation of anisotropy parameter and compressive stress are presented in tabular form