A self-consistent two-dimensional fluid model is employed to investigate the coaxial-coplanar dielectric-barrier discharge (DBD) excited by the sinusoidal voltage in atmospheric helium. Simulation results show that there are two current pulses in the positive half cycle, but only one in the negative half cycle. The discharge is transformed from the Townsend-like mode, through the glow-like mode, and back to the Townsend-like mode in both the positive and negative half cycles, during which the electric field line exhibits an arc-shape profile due to the configuration of coaxial-coplanar electrodes. In the glow-like mode, the cathode fall is located near the inner edge of the ground electrode at the first positive current peak, but close to the outer edge of the ground electrode at the second positive current peak. At the negative current peak, the cathode fall is distributed near the outer edge of the high voltage electrode. Since the instantaneous anode and the instantaneous cathode are on the same side of the discharge space, the dielectric layer is simultaneously covered by positive and negative surface charges due to the movement of charged particles. It is also found that the surface charge density changes significantly on the dielectric layer facing the electrodes. A further study reveals that a stronger discharge always occurs in the central circular area and an alternately complementary discharge takes place in the periphery ring area in the positive half cycle due to the activator-inhibitor effect. This feature is helpful for producing uniform plasma in a whole cycle of DBD. (C)& nbsp;2022 Author(s).