The characteristics of the dielectric barrier discharge (DBD) equipped with asymmetrical electrode (ring electrode on the upper and disk electrode on the lower) in atmospheric helium are investigated by a two-dimensional self-consistent fluid model. Simulation results show that as the applied voltage increases, the discharge enhances and the onset of discharge advances, which is similar to the results of traditional DBD. However, with the applied voltage increasing, the symmetry of the discharge current pulses in the positive and negative half cycles disappears because of the asymmetric electrode configuration. In addition, only the spatial distribution of the electron density at the peak moments of the first and second current pulses satisfies the complementary characteristics, while the spatial distribution at other peak moments does not meet the complementary characteristics. Moreover, the electric field, near the upper dielectric barrier surface, presents a curtain-like distribution with considerable radial electric field components, which results from the non-uniform radial surface charge distribution and the ring electrode configuration. The relative variation of the radial distribution of surface charge density is largely determined by the geometry of the opposite electrode.