  The ANITA experiment has observed two unusual upgoing air shower events which
are consistent with the $\tau$-lepton decay origin. However, these events are
in contradiction with the standard neutrino-matter interaction models as well
as the $\rm EeV$ diffuse neutrino flux limits set by the IceCube and the cosmic
ray facilities like AUGER. In this paper, we have reinvestigated the
possibility of using sterile neutrino hypothesis to explain the ANITA anomalous
events. The diffuse flux of the sterile neutrinos is less constrained by the
IceCube and AUGER experiments due to the small active-sterile mixing
suppression. The quantum decoherence effect should be included for describing
the neutrino flux propagating in the Earth matter, because the interactions
between neutrinos and the Earth matter are very strong at the EeV scale. After
several experimental approximations, we show that the ANITA anomaly itself is
able to be explained by the sterile neutrino origin, but we also predict that
the IceCube observatory should have more events than ANITA. It makes the
sterile neutrino origin very unlikely to account for both of them
simultaneously. A more solid conclusion can be drawn by the dedicated ANITA
signal simulations.
