  Previous researches on high-energy photon events from gamma-ray bursts~(GRBs)
suggest a light speed variation $v(E)=c(1-E/E_{\mathrm{LV}})$ with
$E_{\mathrm{LV}}=3.6\times10^{17}~\mathrm{ GeV}$, together with a pre-burst
scenario that hight-energy photons come out about 10 seconds earlier than
low-energy photons at the GRB source. However, in the Lorentz invariance
violating scenario with an energy dependent light speed considered here,
high-energy photons travel slower than low-energy photons due to the light
speed variation, so that they are usually detected after low-energy photons in
observed GRB data. Here we find four high-energy photon events which were
observed earlier than low-energy photons from Fermi Gamma-ray Space
Telescope~(FGST), and analysis on these photon events supports the pre-burst
scenario of high energy photons from GRBs and the energy dependence of light
speed listed above.
