In the paper, the interaction of an intense relativistic electron beam with the background gas in the high power microwave diode is studied. According to the experimental data, the plasma density generated by impact ionization have been calculated using the numerical methode and particle-in-cell code. The results show that the values of the plasma density produced by impact ionization obtained by the two calculating methods agree well. The ionized plasma densities are 4－12×109cm-3 at the pressures of 0.01 Pa—0.05 Pa. Even considering the two- and three-body recombination effects, the values of the plasma densities produced by impact ionization obtained by the numerical methode and particle-in-cell code still agree well. In addition, the results of PIC simulation show that there is a hump in the plasma density curve with the increasing of pressure. Different from the simple numerical calculation, in calculating the plasma densities, the experimental data are used. The results obtained by the two calculation methodes using the experimental data will be very useful for high power microwave diode and microwave devices.