  We report on an {unusually} bright observation of PSR J1720$-$0533 using the
Five-hundred-meter Aperture Spherical radio Telescope (FAST). The pulsar is in
a black widow system that {was discovered by the Commensal Radio Astronomy FAST
Survey (CRAFTS). By coincidence, a bright scintillation maximum was
simultaneous with the eclipse in our observation which allowed for precise
measurements of flux density variations, as well as dispersion measure (DM) and
polarization.} We found that there are quasi-periodic pulse emission variations
with a modulation period of $\sim$ {22\,s} during the ingress of the eclipse,
which could be caused by plasma lensing. {No such periodic modulation was found
during the egress of the eclipse. } {The linear polarization of the pulsar
disappears before the eclipse, even before there is a visually obvious change
in DM. We also found that the pulse scattering maybe play an important role in
the eclipse of PSR J1720$-$0533.}
