A formalism is proposed to represent a broadband spectrum of Gravity Waves (GWs) via the superposition of a large ensemble of statistically independent monochromatic ones. To produce this large ensemble at a reasonable numerical cost, we use the fact that the life cycles of the waves needed to be parameterized in General Circulation Models (GCMs) have time scales that largely exceed the time step of the model. We can therefore launch few waves with characteristics chosen randomly at each time step, and make them having an effect on a longer time scale by applying an AR1 relation between the gravity waves drag at a given time and that at the next time step. The stochastic GW parameterization is applied to a GCM in the tropics, and its additional drag causes a realistic Quasi-Biennial Oscillation (QBO). The more realistic wind structure also results in a better representation of the large scale equatorial waves, like the Rossby Gravity Waves (RGWs) with periods around 4–5 day.