By using a two-dimensional, full-implicit-continuous-Eulerian (FICE) scheme, we simulated the nonlinear propagation and evolution of gravity wave packets in a compressible, nonisothermal and dissipative atmosphere. The numerical results show that when an upgoing gravity wave packet is generated in the lower mesosphere, it can propagate along its ray path until it reaches lower thermosphere. However, upon reaching the lower thermosphere, the wave packet and associated energy propagate almost horizontally, which departs obviously from the prediction of linear gravity wave theory under WKB approximation in the nondissipative case. Further discussion indicates that the influences of nonlinearity and background temperature are not strong enough to restrict completely the upward energy propagation of the wave packet and that the influence of constant molecular viscosity on the characteristics (energy propagation path and wave parameters) of gravity waves is insignificant. It is the vertical inhomogeneity of molecular viscosity that causes the restriction of upward energy propagation of the gravity wave packet. Moreover, throughout propagation, the dominant vertical wavelength of the wave packet decreases with time, as it is affected by the joint actions of nonlinearity, background temperature, and dissipation. These results indicate that the molecular viscosity, especially the vertical inhomogeneity of molecular viscosity, plays an important role in the nonlinear propagation of gravity wave packets.