We propose a model where sterile neutrinos are introduced to make light neutrinos to be pseudo-Dirac particles. It is shown how tiny mass splitting necessary for realizing pseudo-Dirac neutrinos can be achieved. Within the model, we show how leptogenesis can be successfully generated. Motivated by the recent observation of very high energy neutrino events at IceCube, we study a possibility to observe the effects of the pseudo-Dirac property of neutrinos by performing astronomical-scale baseline experiments to uncover the oscillation effects of very tiny mass splitting. Using the result of global fit to neutrino data for the input of neutrino mixing angles and CP phase at $1\sigma$ C.L. and fixing neutrino energy and mass splittings, we study how the oscillation effects induced by pseudo-Dirac neutrinos may affect the track-to-shower ratio obtained from IceCube data. We also discuss future prospect to observe the effects of the pseudo-Dirac property of neutrinos at high energy neutrino experiments.