Near-inertial waves (NIWs) originate in the ocean upper mixed layer. When they have a large horizontal scale which is characteristic of an atmospheric storm, they are difficult to propagate vertically below the mixed layer. The β-effect and the mesoscale vorticity are considered as two important mechanisms for guiding the downward propagation of near-inertial energy (NIE). In this paper, the effects of “heat pumping” and “cold suction” of typhoons on the ocean stratification are analyzed. It is found that changes in stratification enhance the vertical propagation of NIWs from the mixed layer into the ocean interior on the left side of the typhoon track. To illustrate the impact of stratification changes on both sides of typhoon tracks, the Regional Ocean Modelling System (ROMS) is used to simulate the NIWs generated by Typhoon Kalmaegi in 2014. The results show that, although the wind energy input on the right side of the typhoon track is higher than that on the left side, the NIE injection to the deep ocean from the left side is stronger due to the different dissipation and stratification responses. Our work improves the understanding of the generation, propagation, and dissipation mechanisms of NIWs during typhoons.