The generation of stratospheric gravity waves (GWs) due to typhoon is simulated by using a meso-scale model (WRF) with a typhoon case, the Matsa in 2005. An 8-day model run that covers the major stages of the Matsa's development reproduces the key features of the typhoon. For example, good agreements in the typhoon's track, the intensity, and the spiral clouds, as well as mean state of stratosphere, are seen between the simulation results and the observation. Simulation results clearly show that with typhoon propagates northwestward, pronounced stratospheric GWs are generated continuously in the vicinity of Matsa. The GWs exhibit the typical curve-like wave fronts away from the Typhoon Matsa, and propagate preferentially in the up- stream of the background winds. These characteristics reflect that the stratospheric GWs are closely associated with the ty- phoon, and thus the GWs are referred to as Tropical Cyclone related Gravity Waves (TC-GWs). The results also show that these waves should have a rather large horizontal scale so that the outmost wave fronts can be seen at the distance of ~ 1000 km to the typhoon center in the horizontal plane of 20 kin. This is consistent with the phenomenon of stratospheric TC-GWs with 1000 km horizontal scale disclosed by the previous observational analysis results.