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The ANITA experiment has observed two unusual upgoing air shower events whichare consistent with the $\tau$-lepton decay origin. However, these events arein contradiction with the standard neutrino-matter interaction models as wellas the $\rm EeV$ diffuse neutrino flux limits set by the IceCube and the cosmicray facilities like AUGER. In this paper, we have reinvestigated thepossibility of using sterile neutrino hypothesis to explain the ANITA anomalousevents. The diffuse flux of the sterile neutrinos is less constrained by theIceCube and AUGER experiments due to the small active-sterile mixingsuppression. The quantum decoherence effect should be included for describingthe neutrino flux propagating in the Earth matter, because the interactionsbetween neutrinos and the Earth matter are very strong at the EeV scale. Afterseveral experimental approximations, we show that the ANITA anomaly itself isable to be explained by the sterile neutrino origin, but we also predict thatthe IceCube observatory should have more events than ANITA. It makes thesterile neutrino origin very unlikely to account for both of themsimultaneously. A more solid conclusion can be drawn by the dedicated ANITAsignal simulations.

Sterile neutrinos as a possible explanation for the upward air shower events at ANITA