Abstract: In this paper,the instability,phase velocity and group velocity of the gravitational waves in a geostrophic currents arc analysed by using a two layer model.The conclusions reached arc that:1.When the Froude number is greater than unit,the gravitational waves of some wave lengths will become unstable.This instability may be used to explain the development of some meso-scale systems.2.The group velocity of the gravitational waves can exceed its phase velocity.Therefore,when a meso-scale system is developed in some regions,its energy can travel faster downwind than the phase velocity,therefore a new wave may be formed in the front of the old one.