The paper deals with the propagation of Love waves in a granular medium over an elastic half-space under hydrostatic initial stress due to gravity. The model has been considered to fit with earth having the upper part as granular and the interior as an elastic solid under high initial compressive stress due to gravity. The frequency equation has been obtained and also as particular cases (i) the equation for Love waves in a granular medium over an elastic half-space without gravity field and (ii) the equation for Love waves in an elastic medium over an elastic half-space without gravity field have been obtained. The last result has been shown to tally with the result obtained in Ewing et al. [Elastic Waves in Layered Media (McGraw–Hill, New York, 1957)].