The effect of Quantum Gravity (QG) may bring a tiny light speed variation as $v(E)=c(1-E/E_{rm LV})$, where $E$ is the photon energy and $E_{rm LV}$ 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 $E_{rm LV}=3.6times 10^{17}~rm GeV$ determined by the GRB data.
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