Considering the series effects of high power microwave such as thermal fast electrons effect, collision frequency effect and ionization frequency effect, a unified high power microwave (HPM) propagation model is presented in this paper. A unified air-breakdown model for single-pulse HPM is discussed in detail and the breakdown threshold is determined. It is found that the frequency of plasma induced by high power microwave is greater than previous value. The threshold of air breakdown increases with altitude increasing under the same condition. When the threshold reaches a minimum, a reverse trend will appear. And the minimum value will be obtained in an area of 30-60 km. The typical phenomenon waveform and threshold are gained in the experiment of air breakdown in microwave darkroom. And a well uniform distribution of the air breakdown threshold is shown theoretically and experimentally.