The propagation characteristics of high power microwave pulse in an air-breakdown environment are examined. The maximum electron density produced by microwave air-breakdown is limited to $10^6cm^{-3}$ by the tail-erosion effect. Inorder to increase the electron density, the scheme using two pulses intersecting at a desired height is considered. Increasing the carrier frequency, it is shown that microwave pulse can be transferred without the serious erosion in the numerical simulation. This result is useful for the above scheme. Also, an experiment is conducted to show the tail-erosion effect and confirm that a rapidly generated lossy plasma can cause spectral breaking and frequency shift of a high-power microwave pulse. The experimental results are presented by comparing the frequency spectrum of an incident pulse with that of the pulse transmitted through a self-induced air-breakdown environment. The experimental results show that the amount of frequency upshift is co-related with the ionization rate, whereas that of frequency downshift is correlated with the energy losses from the pulse in the self-generated plasma.