One-dimensional time-dependent numerical simulations are presented to find the discharge mechanism and illustrate the spatio-temporal images of a single streamer in the dielectric barrier discharge (DBD). Calculated results reveal that the three discharge phases of avalanche, streamer, and decay are distinguished depending on the external voltage applied to the electrodes in the DBD. At different over-voltage conditions, the time evolutions of discharge currents show distinct profiles which adequately explain the spatio-temporal variations of the single streamer in the DBD.