We used the Constellation Observing System for Meteorology, Ionosphere, and Climate-2 (COSMIC-2) dry temperature profile data from December 2019 to November 2021 to study the vertical wavenumber spectra of the potential energy of stratospheric gravity waves (GWs Ep) in the Asian monsoon region (15–45°N, 70–150°E). The GW Ep decreases with increasing vertical wavenumber, and the spectral slope varies with wavenumber. The spectral slope becomes smaller over a wavenumber range of 0.1–0.45 km−1, and larger from 0.45–1 km−1, with increasing wavenumber. The energy density distribution at middle and low latitudes shows seasonal variations. Over a wavenumber range of 0.05–0.5 km−1, the energy density in winter is higher at middle latitudes than at low latitudes, and the opposite is observed in summer over a wavenumber range from 0.1 to 1 km−1. Both the spectral amplitude and characteristic wavelength exhibit band-like patterns, and the large-value bands and their centers vary significantly with the season. In winter, the middle latitude spectral amplitude is larger than that at low latitudes, and the significant large-value band-like distribution is at ~40°N. In summer, the distribution is opposite, with large-value band regions over the Bay of Bengal and Indo-China Peninsula. The large-value region of the middle latitude spectral amplitude corresponds to a longer characteristic wavelength, while the large-value region of the low latitude spectral amplitude corresponds to a shorter characteristic wavelength. There is also significant seasonal variation in the distribution of spectral slopes. Over a wavenumber range of 0.1 to 0.5 km−1, the slope is smaller at middle latitudes and larger at low latitudes in winter; the opposite is observed in summer. There is a significant annual cycle of spectral amplitude at middle and low latitudes, and a 4.8 month cycle at middle latitudes.