Abstract: A significant feature of the tropical atmosphere is the positive feedback interaction between cumulus convections and large-scale disturbances.With such a Kind of interaction does CISK theory account for the generation and maintenance of tropical large-scale wave-like disturbances (or equatorial waves).In this paper, cumulus convection heating is parameterized with the vertical velocity at the top of the tropical boundary layer.By making use of a two-layer atmospheric model, the linear stability of the equatorial waves is analyzed.It is shown that in the case where heating magnitude η is O (1), the part of cumulus convection heating parameterized with the low-level horizontal convergence of waves produces only a frequency correction, making no contribution to instable growth rate of the waves; while the part of cumulus convection heating parameterized with the rotational pumping of boundary layer can generate instable equatorial waves.As η> 0.5, equatorial waves become instable under the cumulus convection heating parameterized with the rotational pumping of tropical boundary layer: gravity-type waves all have maximum instable growth rate at a finite wave length, and the growth rates of Rossby-type waves are much greater than those of gravity-type waves.In addition, the cumulus convection heating parameterized with the rotational pumping of tropical boundary layer also produces a frequency correction to equatorial waves.Especially, Kelvin waves become dispersive under such a frequency correction.