Abstract: A simple baroclinic semi-geostrophic model on an equatorial β-plane is employed the effects of the vertical shearof the basic zonal geostrophic flow and the variation of the basic potential temperature on the longequatorial Rossby waves.Adimensionless parameter σ is introduced to represent the variation of basic potintial temperature field, in the thermody namics equation.Theoretical analyses show that the vertical shearof the basic flow will cause instability of the longequatorial Rossby waves and affectthe po pagation speed of the Rossby waves.