In the present work, a mathematical modeling of propagation of Love waves in dry sandy layer under initial stress above anisotropic porous half-space under gravity is reported. The equation of motion for the Love wave has been formulated following Biot, using suitably chosen boundary conditions at the interface of sandy layer and porous half-space under gravity. The dispersion equation of phase velocity of this proposed multilayer ground structure has been derived following the Whittaker function and its derivative, which is further expanded asymptotically, retaining the terms up to only the second degree for large argument due to small values of Biot's gravity parameter (varying from 0 to 1). The study reveals that the gravity and porosity of the porous half-space play important roles on the propagation of Love waves. It is observed that with the increase in gravitation parameter and porosity of the half-space, the phase velocity of the Love wave decreases, whereas the velocity of the waves increases for the increase in the value of the sandy parameter. The effects of these above-mentioned medium parameters for isotropic and anisotropic cases are studied on the propagation of Love waves, and their numerical results have been presented graphically.