We conduct a mesoscale simulation with a 4-km resolution for Hurricane Joaquin in 2015 using the Weather Research and Forecast (WRF) model. The model data are used to study stratospheric gravity waves (GWs) generated by the hurricane and how they correlate with hurricane intensity. The simulation results show spiral GWs propagating upward and anticlockwise away from the hurricane center. GWs with vertical wavelengths up to 14 km are generated. We find that GW activity is more frequent during hurricane intensification than during weakening, particularly for the most intense GW activity. There is a significant time offset between the appearance of intense stratospheric GWs and hurricane intensification. Therefore, the emergence of intensive stratospheric GW activity may be considered a useful proxy for identifying hurricane intensification.