Abstract: By using an ADI scheme, the nonlinear propagation of downgoing gravitywave packet in a two-dimensional compressible atmosphere is simulated. Results of numerical simulation suggest that the wave-associate energy moves downward and the velocity perturbation amplitude decreased rapidly. Comparing with the numerical results of linearized equations, we find that under nonlinear condition, a gravity wave packet is still able to keep some characterizations as under linear propagation. The impact of nonlinear effect on the propagation velocity of gravitywave packet weakens rapidly with decreasing velocity perturbation amplitude.