Abstract: In this paper, a numerical simulation of the geostrophic adjustment process with a C-grid network is illustrated. A difference scheme which has the energy and potential vorticity conserving relation consistent with the differential equations is given, and the effect of some time difference schemes on dispersion of the gravity-inertia wave is discussed. An improved forward backward time integration scheme is proposed for keeping the computational stability. The effect of various boundary conditions for a finite region model on the gravity-inertia wave is shown by some calculated results.