The interaction between the plasma and the high power microwave was studied with the wave equation, the electron transport equation and the heavy species transport equation. The change process of the electron density and the electric field in the plasma was calculated, and the dispersion effect of the incident frequency in the interactions was especially analyzed. Result shows that the electron density and the electric field intensity will change suddenly due to the interactions of HPM(high power microwave) and plasma, in which the mean electron density will increase from 1×10⁹ m^-3 to 1×10¹⁹m^-3, and the average electric field strength will decrease from the original value to zero abruptly in a very short time. Moreover, the threshold field strength and minimum generation time in the changing process are considered to study the dispersion effects. As a result, the threshold strength and generation time are vary with the frequency. In addition, it can be admitted that the threshold strength increases linearly and the generation time grows nonlinearly with the frequency of incident wave with further research.