Whereas discharge characteristics of a gliding arc have previously been investigated in a low-speed subsonic flow without considering the effect of shock waves and extremely high turbulence, we here studied an important physical feature of the gliding arc in a supersonic flow that generates complex shock waves and extremely high turbulence. The gliding arc in a 1.2 Mach supersonic jet air flow is investigated by high-speed imaging, schlieren imaging, electrical measurements, and the large eddy simulation. The experimental results show that high-repetition transitions between the spark-type discharges and the glow-type discharge with a frequency of 1.4–2.1 MHz can be observed in the supersonic flow after the gliding arc is generated between the narrowest gap of knife-shaped electrodes, whereas the similar phenomena are invisible in a low-speed subsonic flow. It can be recognized that the high-repetition transitions occur in the region with complex structures of shock waves and expansion waves. The large velocity/density gradient generated by the complex wave structures and the small-scale vortices produced by the strong turbulence is located near the position where the high-repetition transitions occur. The high-repetition transitions between the spark-type discharges and the glow-type discharges are found to be mainly caused by the combined effects of the strong turbulent eddy transportation in the supersonic flow and the drastic change in the flow properties across the shock wave, shedding light on the mechanism of the high-repetition discharge transitions of the gliding arc in a supersonic flow.