A self-consistent 2-D fluid simulation model is used to simulate dielectric barrier discharge (DBD) in the air of a wire-cylinder structure at atmospheric pressure. By solving the electron-ion transport equation, diffusion equation, and boundary conditions of the plasma, the numerical results of discharge and plasma characteristics are obtained, and the accuracy is verified. The results show that there are two current pulses during a typical cycle, in the voltage rising and falling stages, and that the peak values of these two pulses differ because of the asymmetry of the electrode structure. By analyzing the evolution of the 1-D and 2-D distributions of the electric field and particle densities, the characteristics of typical glow discharge at the moment of the current pulse are shown: cathode fall, negative glow, and a plasma positive column. The entire discharge process starts with Townsend discharge, evolves to glow discharge at the moment of the current pulse, and gradually returns to Townsend discharge after the end of the current pulse. The distribution of electrons and ions at the moment of the current pulse is demonstrated, and the variation in charge accumulation on the surface of the medium is calculated. Surface charge accumulation has a periodic symmetric distribution and is divided into four main stages: positive charge neutralization, negative charge accumulation, negative charge neutralization, and positive charge accumulation.