In this paper, a planar atmospheric-pressure dielectric barrier discharge (AP-DBD) of nitrogen mixed with ammonia (0-2 %) is simulated using one-dimensional self-consistent fluid modeling with cell-centered finite-volume method. This AP-DBD is driven by a 30 kHz power source with distorted sinusoidal voltages. The simulated discharge current densities are found to be in good agreement with the experiment data in both phase and magnitude. The simulated results show that the discharges of N-2 mixed with NH3 (0-2 %) are all typical Townsend-like discharges because the ions always outnumber the electrons very much which leads to no quasi-neutral region in the gap throughout the cycle. N-2 (+) and N-4 (+) are found to be the most abundant charged species during and after the breakdown process, respectively, like a pure nitrogen DBD. NH4 (+) increases rapidly initially with increasing addition of NH3 and levels off eventually. In addition, N is the most dominant neutral species, except the background species, N-2 and NH3, and NH2 and H are the second dominant species, which increase with increasing added NH3. The existence of abundant NH2 plays an important role in those applications which require functional group incorporation.