We found that generation of a homogeneous dielectric barrier discharge (DBD) in atmospheric-pressure air was possible at the frequency range from 32 Hz to 1.1 kHz using alumina (Kyocera A473) as a barrier material. In this homogeneous DBD, the discharge current was continuous with no pulse, and the luminosity became strong near the anode surface. Therefore, this homogeneous DBD is an atmospheric-pressure Townsend discharge (APTD) characterized by electron avalanche ( effect) and secondary electron emission from the barrier material ( effect). We also found that there is a domain in frequency and voltage of the stable generation of the APTD in air. This domain becomes wider with the increase of the ac frequency. If the applied voltage is a bit higher than the upper voltage limit of the stable generation of the APTD, the discharge mode changes from the APTD mode to an oscillation mode. In order to clarify the decisive factor of the generation of the low-frequency APTD, we investigated the influence of gaseous species (oxygen, nitrogen, and helium) and barrier materials (alumina and soda glass). From these experiments, we found that gaseous species are not a decisive factor in the stable generation of the low-frequency APTD, because the low-frequency APTD is generated in all gases tested. Here, the generation of the APTD in 99.5% oxygen may be the first achievement. On the other hand, we found that the barrier material plays an important role in the stable generation of the low-frequency APTD. This paper describes the detail of the experimental results and discussions of the low-frequency APTD.