The onset time of buoyancy-driven instability in a saline solution where evaporation proceeds through the solution-air interface is analyzed theoretically and numerically. Based on linear stability theory, new stability equations are derived and numerically solved. Also, nonlinear numerical simulations are conducted using FEM solver, COMSOL Multiphysics.® It is clearly shown that as the evaporation proceeds, the height of solution continuously decreases with time. Moreover, as the evaporation proceeds, concentrated saline solution near the evaporating surface induces gravitational instability. The critical time determined from the linear stability analysis explains the numerical simulation results reasonably. The present theoretical and numerical studies present that evaporation-driven instability is governed by the dimensionless evaporation rate, α, and the initial salt concentration, Ra. The present numerical simulations explain the previous experimental plume dynamics in the evaporation-driven instability systems quite well.