Periodic and spontaneous on-off oscillation belongs to the onset and damping behaviors of thermoacoustic engines, and investigations on this phenomenon lead to better operation of the thermoacoustic engines with stable performances. In this paper, the quasi- periodic on-off oscillation in a small-scale traveling wave thermoacoustic heat engine with a resonator length of only 1m was experimentally investigated. The type of working media, mean pressure and the input heating power are the main operating parameters, which significantly affect the formation of the periodic on-off oscillation. The experimental results demonstrated there was a critical charge pressure over which the periodic on-off oscillation could happen. For the small- scale engine with helium gas as the working media, the mean pressure threshold value was about 1.4MPa and the on-off oscillation occurred with a single frequency. Using nitrogen and argon gas as the working media, the on-off oscillation was not observed. The reason was qualitatively analyzed as well.