This paper aims to study the dispersion of torsional surface waves in a non-homogeneous anisotropic layer over heterogeneous half-space. We consider the inhomogeneity varies exponentially with depth in the layer and in half-space three types of heterogeneities, namely, quadratic, hyperbolic and exponential are assumed. The dispersion equation has been deducted for each case in a closed form by means of variable separable method. It has been observed that for homogeneous isotropic upper layer over a homogeneous half-space, the velocity of torsional surface waves coincides with that of Love waves. Dispersion curves are plotted for different variation in inhomogeneity parameters. The effects of the medium characteristics on the propagation of torsional surface waves are discussed.