The formation and propagation of pseudo-filamentary dielectric barrier discharge in atmospheric air are investigated through a 2D fluid model. The discharge development can be divided into three stages: the volume streamer stage, the surface streamer stage, and the reverse discharge stage. The simulations show that the streamer head becomes wider and the electron density of the volume streamer head increases six times when the volume streamer interacts with the dielectric, and the volume streamer transforms into the surface streamer after the interaction. Compared with volume streamers, surface streamers have a smaller radius, a higher electric field, and a higher electron density. Furthermore, the parameters that may influence the discharge characteristics are also studied. It is found that a larger dielectric permittivity, a thinner dielectric, or a shorter voltage rise time leads to earlier inception of volume streamers, faster propagation of surface streamers, and higher current density. It is observed that the velocity of the surface streamer increases first, and then, decreases with the accumulated charges on the surface.