Abstract: The nonlinear propagation of high-power microwave Gaussian beam in the atmosphere is studied. An appropriate model is presented for calculating the air refractive index when HPM Gaussian beam propagates in the atmosphere. In this model, the cross-section area is treated as a number of concentric annulus, and assuming each has a uniform electric field intensity distribution. Based on the knowledge of air breakdown and the theory of the propagation of Ganssian beam, the air refractive index is calculated for different field intensity, frequency of microwave, width of pulse, pressure, when giving parameters of the Gaussian beam. Then the curves of temporal spatial dispersion are given in the paper. The air breakdown is discussed based on the calculations and some useful results have been obtained.