  The constancy of light speed is a basic assumption in Einstein's special
relativity, and consequently the Lorentz invariance is a fundamental symmetry
of space-time in modern physics. However, it is speculated that the speed of
light becomes energy-dependent due to the Lorentz invariance violation~(LV) in
various new physics theories. We analyse the data of the energetic photons from
the gamma-ray bursts (GRBs) by the Fermi Gamma-Ray Space Telescope, and find
more events to support the energy dependence in the light speed with both
linear and quadratic form corrections. We provide two scenarios to understand
all the new-released Pass~8 data of bright GRBs by the Fermi-LAT Collaboration,
with predictions from such scenarios being testable by future detected GRBs.
