In this study, we have proposed the auxiliary bias pulse scheme to improve the stability of atmospheric pressure plasma jets driven by an AC sinusoidal waveform excitation source. The stability of discharges can be significantly improved by the compensation of irregular variation in memory voltage due to the effect of auxiliary bias pulse. From the parametric study, such as the width, voltage, and onset time of auxiliary bias pulse, it has been demonstrated that the auxiliary bias pulse plays a significant role in suppressing the irregular discharges caused by the irregular variation in memory voltage and stable discharge can be initiated with the termination of the auxiliary bias pulse. As a result of further investigating the effects of the auxiliary pulse scheme on the jet stability under various process conditions such as the distance between the jet head and the counter electrode, and carrier gas flow, the jet stability can be improved by adjusting the amplitude and number of the bias pulse depending on the variations in the process conditions.