It is difficult in measuring the electron density of an atmospheric air spark shock wave plasma jet, due to its variation on the time scale of sub-microseconds. In this paper, the time-varying electron density of air spark shock wave plasma jet is measured, based on the principle of microwave Rayleigh scattering. The system constant A is determined by using calibration of materials with known properties; the results show that the system constant is obtained as A = 1.04 × 10⁵ V·Ω·m^–2. According to the principle of microwave Rayleigh scattering, the electron density of the plasma jet is related to its radius and length of the plasma jet plume. Combined with the discharge image captured by ICCD camera, it is observed that the plasma jet plumes are with irregular patterns. In order to facilitate the calculation, the plasma jet plumes are replaced by cylinders with the same volume as the original shapes. Thus, the equivalent radius and length of the plasma jet plume are obtained. According to the known data, the electron density is determined to be in the order of 10²⁰ m^–3; its value increases rapidly to the peak value, and after then exponential attenuates along with time. In addition, the effect of different equivalent dimensions of the plasma jet plume on the measurement results is also discussed. It is shown that the calculation result with the time-varying equivalent radius and the time-varying equivalent length is the most effective one. In addition, the first fast peak is caused by the ionization wave of the photo ionization. The actual ionization process is that the air discharge in the cathode cavity releases a large number of high energy photons, which pass through the cathode nozzle and project into the region outside the nozzle; and then the O₂ molecule in the ambient air are ionized by those high energy photons to form the plasma jet plume at the time of 1 μs.