According to Einstein's relativity,the speed of light is a constant in free space.However,it is speculated from quantum gravity that the light speed may receive a correction in powers of E/Epl,where E is the energy of the photon and Ep1 =√hc5/G ≈ 1.22 × 1019 GeV is the Planck energy.Therefore the light speed might be energy dependent due to the Lorentz invariance violation (see,e.g.,Refs.[1-6]).Such speed variation is very tiny and can hardly be detected on the earth.It was suggested by Amelino-Camelia et al.[7] that photons from gamma-ray bursts (GRBs) can be used to detect the light speed variation.