Abstract: By using an Alternative-Direction-Implicit （ADI） scheme, a numerical model for nonlinear propagation of gravity-wave packets in a three-dimensional compressible atmosphere is solved. Results of numerical simulation show that after several periods, the gravity-wave packets propagate steadily upward and keep its shape well. The interior points and boundaries of the calculating region are stable. During the propagation the amplitude of wave-associated perturbation velocities increase with the increasing height. This shows that ADI scheme is reliable for simulating the nonlinear propagation of gravity-wave packets in a three-dimensional compressible atmosphere. From the results, It’s also found that under nonlinear condition, a gravity wave packet is still able to keep some characterizations as under linear propagation. The nonlinear effect mainly impacts the propagation velocity of gravity-wave packets.