  Based on recent proposal to associate IceCube TeV and PeV neutrino events
with gamma-ray bursts~(GRBs) by considering the Lorentz violation of neutrinos,
we provide a new estimate on the GRB neutrino flux and such result is much
bigger than previous results by the IceCube Collaboration. Among these 24
neutrino ``shower" events above 60~TeV, 12 events are associated with GRBs.
Such result is comparable with the prediction from GRB fireball models.
Analysis of track events provide consistent result with the shower events to
associate high energy cosmic neutrinos with GRBs under the same Lorentz
violation features of neutrinos. We also make a background estimation and
reveal GRBs as a significant source for the ultra-high energy IceCube neutrino
events. Our work supports the Lorentz violation and $CPT$-violation of
neutrinos, indicating new physics beyond relativity.
