A two-dimensional fluid model was used to investigate the characteristics of a multiple-current-pulse dielectric barrier discharge (DBD) equipped with ring electrodes in helium at atmospheric pressure. The simulation results show that the discharge at peak moment follows the Townsend mode in the DBD with two current pulses in each half cycle. However, when there are three or four current pulses in each half cycle, the discharge mode at the first current peak transforms to the glow mode. Additionally, for the first and third current pulse, the breakdown first occurs in the radial center of the ring electrodes. But for the discharge in the second and fourth current pulse, it ignites from the periphery of the ring electrodes. Moreover, the discharge structure, i.e., the radial spatial distributions of current density, electron density, and electric field at peak moments, shows a feature of alternation between (1) higher current density, electron density, and electric field locating in the radial center of ring electrodes (center-advantage) and (2) higher current density, electron density, and electric field locating in the periphery of ring electrodes (periphery-advantage). This behavior is attributed to the fact that non-uniform surface charge accumulation during the previous discharge has different effects on the electric field in the gas gap in the subsequent discharge. Published under license by AIP Publishing.