Concentric gravity waves (CGWs) in the middle and upper atmosphere show wave-coupling processes between the lower atmosphere and the middle and upper atmosphere. In this research, we analyzed a case of CGWs detected simultaneously by the AIRS (Atmospheric Infrared Sounder) and the VIIRS/DNB (Day/Night Band of the Visible Infrared Imager Radiometer Suite) in the stratosphere and mesosphere. Results showed that gravity waves (GWs) were generated by the collocated Hurricane Bejisa on the island of Mauritius. The AIRS data showed arc-like phase fronts of GWs with horizontal wavelengths of 190 and 150 km at 21:08 coordinated universal time (UTC) on 1 January 2014 and at 10:00 UTC on 2 January 2014, whereas the DNB observed arced GWs with horizontal wavelengths of 60 and 150 km in the same geographic regions at 22:24 UTC. The characteristics of CGW parameters in the stratosphere (~40 km) and the mesosphere (~87 km), such as the vertical wavelength, intrinsic frequency, and intrinsic horizontal phase speed, were first derived together with the background winds from ERA5 reanalysis data and Horizontal Wind Model data through the dispersion relationship of GWs and the wind-filtering theory.