Natural gas hydrate is a new energy source with great potential. Studying the seismic response characteristics of natural gas hydrate in permafrost area is crucial to the exploration and development of natural gas hydrate in China's land area. Based on the Kelvin viscoelastic media model, our work establishes a theoretical geological-geophysical model based on the actual geological and stratigraphic conditions of the Qilian Mountain permafrost, uses the staggered-grid finite difference method to perform forward numerical simulation, and performs wave field characteristic analysis and instantaneous seismic attribute extraction of self-excitation and self-receiving seismic records. The results show that the reflected amplitude energy is weaker when the seismic wave passes through the gas hydrate formation. In the range where the instantaneous frequency attribute profile can distinguish the layer thickness, the instantaneous frequency decreases marginally with the increase of the layer thickness. When seismic waves pass through natural gas-bearing formations, the reflected waves show strong reflection characteristics, and the instantaneous frequency energy increases. The instantaneous seismic attribute has better resolution for the wave-impedance interface, especially the instantaneous phase attribute profile. Therefore, the comprehensive analysis of the instantaneous attribute characteristics can provide a basis for the identification and prediction of terrestrial gas hydrates.