•We analyze the data of photons from gamma-ray bursts (GRBs) with energies higher than 10 GeV.•We unveil a surprising regularity behind the data of these energetic photons.•Such regularity can serve to support the energy-dependence of light speed in cosmological space. Display omitted The effect of quantum gravity can bring a tiny light speed variation which is detectable through energetic photons propagating from gamma ray bursts (GRBs) to an observer such as the space observatory. Through an analysis of the energetic photon data of the GRBs observed by the Fermi Gamma-ray Space Telescope (FGST), we reveal a surprising regularity of the observed time lags between photons of different energies with respect to the Lorentz violation factor due to the light speed energy dependence. Such regularity suggests a linear form correction of the light speed v(E)=c(1−E/ELV), where E is the photon energy and ELV=(3.60±0.26)×1017GeV is the Lorentz violation scale measured by the energetic photon data of GRBs. The results support an energy dependence of the light speed in cosmological space.