The effects of gravity modulation on the instability of double-diffusive convections in a horizontal tank with aspect ratio (width/height) of 11 have been investigated by experiments and numerical simulations. The stably stratified fluid layer is set up with ethanol-water solution of 0.0 and 2.0% (by weight). The tank is fixed on a platform that can oscillate in the vertical direction. A constant temperature difference is maintained across the tank at thermal Rayleigh number . The fluid layer becomes unstable as the initially stable solute gradient slowly decreases due to the non-diffusive boundary conditions. The experiments determine that the instability onset under steady gravity is at with onset vortices of wavelength and oscillatory frequency . When the tank is oscillated at modulation frequency and amplitude , the fluid layer is destabilized slightly with a critical and onset vortices of and . A two-dimensional numerical simulation has accurately reproduced the experimental results of steady gravity, and demonstrated that the slight destability effect of gravity modulation is contributed by the asymmetry of the actual gravity modulation.Further simulations have yielded following results: (1) Under steady gravity, the kinetic energy and mechanical work components oscillate synchronously with . Under modulated gravity, they only oscillate synchronously with when is low, whereas not only synchronously with locally but also synchronously with globally when is high; (2) The resonance phenomenon predicted by Chen (2001) also exists under the present lab conditions. Such instability is in the sub-harmonic mode and the destability effect increases as increases. (3) The double-diffusive fluid layer may experience density-mode instability before the double-diffusive instability onset at certain and . Such density-mode instability is generally in the sub-harmonic mode, although it may be in the synchronous mode when is low and is large. This instability accelerates the mixing of the density gradient across the fluid layer and thus affects the succeeding double-diffusive instability; (4) When the background gravity is absent, the purely modulated gravity destabilizes the fluid layer when is low. On the contrary, it stabilizes the fluid layer when is high and the instability onset is in the synchronous mode.