Atmospheric wave transport momentum from lower to higher altitudes and have important effects on the general circulation. Typhoon is a significant source of stratospheric gravity waves. The purpose of this study is to investigate the propagation direction, wavelength and period of the typhoon-induced gravity waves with the numerical model and validate its simulation capability by satellite observations. The WRF model is used to reconstruct the Typhoon "Muifa" (2011). The gravity wave parameters including horizontal wavelengths, vertical wavelengths and periods are estimated by the three-dimensional FFT wave spectrum analysis. The AIRS observations data is used to analyze the stratospheric gravity wave features and validate the model outputs. The vertical velocity field from model outputs shows that the typhoon has the energy to induce gravity waves nearly in all directions of the troposphere, while in the stratosphere the waves are only concentrated in the east of the typhoon center, and the range can reach 1000 km when the gravity waves propagate to the stratosphere. In addition, the stratospheric gravity waves and the spiral rain bands have some similarities in the pattern, location and scale. Furthermore, the wind analysis indicates that the differences of gravity waves at different heights mainly result from the modulation of westward background wind and wind shear, which happens in the process of vertical propagation. It reveals that the gravity waves mainly propagate against the background wind field. Then the FFT wave spectral analysis reveals that the gravity wave has the horizontal wavelengths of approximately 1000 km, the periods of 15 similar to 25 h, and the vertical wavelengths of 8 similar to 12 km at 25 km height. At last,. AIRS observations show semicircular arc waves at 30 similar to 40 km height, which are similar to those shown at lower heights in the WRF model. This study indicates that the WRF model can reasonably reproduce the stratospheric gravity waves in terms of pattern, propagation and scope. It also reveals' that the data from different techniques are complementary for stratospheric gravity wave analysis. Finally, the AIRS observations show great application potential in stratospheric gravity waves analysis.