The influence of background ionization on the ignition dynamics of the pulsed plasma plume is studied. The ignition delay time of each pulse is investigated by recording the voltage signal and the light emission signal. By changing the frequency, the relationship between the pulse-off time and the ignition delay time is revealed. This indicates that residual active species produced in the previous discharge play a role in the next one. With the decrease in the frequency, both time delay and ignition delay time increase. This is due to the decay of the reactive species densities in the pulse-off time. Lower concentrations of these species lead to a longer ignition delay time. The functions for calculating the ignition delay time are utilized to explain the effect of residual species. The independent data of each discharge also evidence the impact of the previous pulse. The exotic relationship between the ignition delay times of the first two pulses may be due to the electrode configuration used in this work. For a pin-to-plane electrode structure, the active species produced during the breakdown are accumulated around the anode (pin-point) where the discharge initiated for the asymmetrical electric field distribution.