We interpret the neutrino anomalies in neutrino oscillation experiments and the high energy neutrino events at IceCube in terms of neutrino oscillations in an extension of the standard model where three sterile neutrinos are introduced so as to make two light neutrinos to be Pseudo-Dirac particles and a light neutrino to be a Majorana particle. Our model is different from the so-called 3 + n model with n sterile neutrinos suggested to interpret short baseline anomalies in terms of neutrino oscillations. While the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix in 3 + n model is simply extended to n × n unitary matrix, the neutrino mixing matrix in our model is parameterized so as to keep the 3 × 3 PMNS mixing matrix for three active neutrinos unitary.There are also no flavor changing neutral current interactions leading to the conversion of active neutrinos to sterile ones or vice versa. We derive new forms of neutrino oscillation probabilities containing the new interference between the active and sterile neutrinos which are characterized by additional new parameters ∆m 2 and θ. Based on the new formulae derived, we show how the short baseline neutrino anomalies can be explained in terms of oscillations, and study the implication of the high energy neutrino events detected at IceCube on the probe of pseudo-Dirac neutrinos. New phenomenological effects attributed to the existence of the sterile neutrinos are discussed. The observation of neutrino oscillations in the atmospheric neutrino 1 Super-Kamiokande [3], the solar neutrino 2 SNO [5], and the reactor neutrino Daya Bay[6] and RENO [7] 3 experiments is one of big discoveries in particle physics since 90's. It implies that neutrinos are massive particles and that the three flavor neutrinos ν e , ν µ , ν τ are mixtures of neutrinos with definite masses ν i (with i = 1, 2, ...). Although neutrino oscillations among three active neutrino flavors have been confirmed by the analysis based on the experiments mentioned above, there exist several anomalies which are unexpected results coming from short baseline (SBL) experiments such as the reactor antineutrino anomaly [9], the Gallium solar anomaly [10,11], and the Liquid Scintillator Neutrino Detector (LSND) anomaly [12] (including MiniBooNE anomaly [13]). To resolve those neutrino anomalies in terms of neutrino oscillation, it is required to introduce at least one additional squared-mass difference, ∆m 2 SBL , which is much larger than ∆m 2 Sol and ∆m 2 Atm [9]. This result suggests indication in favor of the possible existence of eV-mass sterile neutrino.Apart from the anomalous results in accelerator and reactor based neutrino experiments favoring the existence of light sterile neutrino, IceCube experiments [14] announced the observation of vey high energy neutrino events. The study for the track-to shower ratio of the subset with energy above 60 TeV coming from IceCube has shown that the events are consistent with the hypothesis that cosmic neutrinos have been seen even though their origin and propagation are stil...