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High-power atmospheric glow discharges (APGDs) are widely used in various industrial applications. Transient glow microdischarges in ambient air also serve as a plasma source for microprocessing technology. In this study, we developed novel driving technique of the transient glow microdischarge with miniature helium gas flow powered by high-voltage pulse train. It was obtained by using the burst pulse generator with a nonlinear transmission line (NLTL), which consisted of chip monolithic ceramic capacitors as nonlinear elements. Repetitive burst pulses with an output voltage of 2.2 kV and a pulse width of 40 ns were generated. The equivalent frequency of the pulse train was 12.5 MHz. A stabilization effect of the highly repetitive operation on the discharge was confirmed regardless of a short residential time of a helium gas.