The single pulses of PSR J1921+1419 were examined in detail using high-sensitivity observations from the Five-hundred-meter Aperture Spherical radio Telescope (FAST) at a central frequency of 1250 MHz. The high-sensitivity observations indicate that the pulsar exhibits two distinct emission modes, which are classified as strong and weak modes based on the intensity of the single pulses. In our observations, the times spent in both modes are nearly equal, and each is about half of the total observation time. The minimum duration of both modes is $1\,P$ and the maximum duration is $13\,P$, where P is the pulsar spin period. Additionally, the mean intensity of the weak mode is less than half of that of the strong mode. Notably, the switching between these modes demonstrates a clear quasi-periodicity with a modulation period of approximately $10 \pm 2\,P$. An analysis of the polarisation properties of both modes indicates that they originate from the same region within the magnetosphere of the pulsar. Finally, the viewing geometry was analysed based on the kinematical effects.