The effect of Quantum Gravity ( QG ) may bring a tiny light speed variation as v ( E ) = c ( 1 - E / E _ { LV } ) , where E is the photon energy and E _ { LV } is a Lorentz violation scale .
A remarkable regularity was suggested in previous studies to look for the light speed variation from high energy photon events of Gamma Ray Bursts ( GRBs ) .
We provide a general analysis on the data of 25 bright GRBs observed by the Fermi Gamma-ray Space Telescope ( FGST ) .
Such method allows a completed scan over all possibilities in a more clean and impartial way without any bias compared to previous intuitive analysis .
The results show that with the increase in the intrinsic energies of photons , such regularity truly emerges and gradually becomes significant .
For photons with intrinsic energies higher than 40 GeV , the regularity exists at a significance of 3-5 \sigma with E _ { LV } = 3.6 \times 10 ^ { 17 } ~ { } GeV determined by the GRB data .