The plasma jet wind tunnel, as a ground simulation device for studying the electromagnetic properties of near-space vehicle sheaths, can help people conduct several studies, such as communications and electronic parameter diagnostics. The plasma produced by a plasma generator has time-dependent variations due to the influence of power supply oscillations, turbulence, and other aspects of the device. To accurately define the experimental state of plasma, it is necessary to carefully analyze the three-dimensional (3D) time-varying characteristics of the plasma jet accurately since the distribution is non-uniform. This paper uses volume tomography technology to reconstruct the time series of the 3D emission field of the plasma jet with high-speed cameras. Then, the time–frequency characteristics, overall instability of the emission intensity, central axis position, and shape of the plasma jet are analyzed. The following characteristics are mainly observed: First, the plasma generator ejects plasma intermittently, which then spirals forward away from the nozzle. Second, the intensity, the radius of central axis movement, and the shape of the plasma jet vary with time at the same low frequency. The magnitude of this frequency is mainly related to the rate of change of the jet's air pressure difference with the vacuum chamber. Third, the overall instability of the plasma jet increases along the axial direction away from the nozzle and radially away from the center of the jet.