  The compact X-ray binary system Cyg X-3 has been recently discovered as a
source of GeV gamma-rays by the AGILE and the {\it Fermi} satellites. It shows
emission features in the GeV gamma-rays similar to other gamma-ray binaries
which were also observed in the TeV gamma-rays (LS 5039 and LSI +61 303). The
question appears whether Cyg X-3 can be also detected in the TeV gamma-rays by
the Cherenkov telescopes.
  Here we discuss this problem in detail based on the anisotropic inverse
Compton (IC) e-p pair cascade model successfully applied to TeV gamma-ray
binaries. We calculate the gamma-ray light curves and gamma-ray spectra
expected from the cascade process occurring inside the Cyg X-3 binary system.
It is found that the gamma-ray light curves at GeV energies can be consistent
with the gamma-ray light curve observed by the Fermi for reasonable parameters
of the orbit of the injection source of relativistic electrons. Moreover, we
show that in such a model the sub-TeV gamma-ray emission (above 100 GeV) is
expected to be below sensitivities of the present Cherenkov telescopes assuming
that electrons are accelerated in Cyg X-3 to TeV energies. The next stage
Cherenkov telescopes (MAGIC II, HESS II) should have the energy threshold in
the range 20-30 GeV, in order to have a chance to detect the signal from Cyg
X-3. Otherwise, the positive detection of gamma-rays at energies above a few
tens of GeV requires a telescope with the sensitivity of ~0.1% of Crab Units.
We conclude that detection of sub-TeV gamma-rays from Cyg X-3 by on-ground
telescopes has to probably wait for construction of the Cherenkov Telescope
Array (CTA).
