A recent proposal to associate 60 TeV to 2 PeV IceCube neutrino events with gamma-ray bursts ( GRBs ) indicates the Lorentz violation of cosmic neutrinos and leads further to the CPT symmetry violation between neutrinos and antineutrinos . Here we find that another 12 northern hemisphere track events possibly correlated with GRBs from three-year IceCube data satisfy the same regularity at a lower energy scale around 1 TeV . The combined fitting indicates a Lorentz violation scale { E } _ { LV } = ( 6.4 \pm 1.5 ) \times 10 ^ { 17 } ~ { } { GeV } and an intrinsic time difference { \Delta { t } _ { in } = ( -2.8 \pm 0.7 ) \times 10 ^ { 2 } ~ { } { s } } , from which we find an earlier emission of neutrinos than photons at the GRB source . We also suggest analyzing neutrino events detected a few minutes before the GRB trigger time to test the CPT violation of ultrahigh-energy neutrinos .