Modelling of SH-waves in an anisotropic fiber-reinforced layer provides a great deal of support in the understanding of seismic wave propagation. This paper deals with the propagation of SH-waves in a fiber-reinforced anisotropic layer over a pre-stressed heterogeneous half-space. The heterogeneity of the elastic half-space is caused by linear variations of density and rigidity. As a special case when both media are homogeneous and stress free, the derived equation is in agreement with the general equation of the Love wave. Numerically, it is observed that the velocity of SH-waves decreases with an increase in heterogeneity-reinforced parameters and decrease in initial stress.